This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.
PI.1: : Constant Velocity
PI.1.1: : Develop graphical, mathematical, and pictorial representations (e.g. a motion map) that describe the relationship between the clock reading (time) and position of an object moving at a uniform rate and apply those representations to qualitatively and quantitatively describe the motion of an object.
Distance-Time and Velocity-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.5 Minute Preview
PI.1.2: : Describe the slope of the graphical representation of position vs. clock reading (time) in terms of the velocity of the object.
Distance-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs.5 Minute Preview
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.5 Minute Preview
PI.1.3: : Rank the velocities of objects in a system based on the slope of a position vs. clock reading (time) graphical representation. Recognize that the magnitude of the slope representing a negative velocity can be greater than the magnitude of the slope representing a positive velocity.
Distance-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs.5 Minute Preview
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.5 Minute Preview
PI.1.4: : Describe the differences between the terms “distance,” “displacement,” “speed,” “velocity,” “average speed,” and “average velocity” and be able to calculate any of those values given an object moving at a single constant velocity or with different constant velocities over a given time interval.
Distance-Time and Velocity-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.5 Minute Preview
PI.2.1: : Develop graphical, mathematical, and pictorial representations (e.g. a motion map) that describe the relationship between the clock reading (time) and velocity of an object moving at a uniformly changing rate and apply those representations to qualitatively and quantitatively describe the motion of an object.
Atwood Machine
Measure the height and velocity of two objects connected by a massless rope over a pulley. Observe the forces acting on each mass throughout the simulation. Calculate the acceleration of the objects, and relate these calculations to Newton's Laws of Motion. The mass of each object can be manipulated, as well as the mass and radius of the pulley.5 Minute Preview
Fire a banana cannon at a monkey in a tree. The monkey drops from the tree at the moment the banana is fired from the cannon. Determine where to aim the cannon so the monkey catches the banana. The position of the cannon, launch angle and initial velocity of the banana can be varied. Students can observe the velocity vectors and the paths of the monkey and banana.5 Minute Preview
Investigate the motion of an object as it falls to the ground. A variety of objects can be compared, and their motion can be observed in a vacuum, in normal air, and in denser air. The position, velocity, and acceleration are measured over time, and the forces on the object can be displayed. Using the manual settings, the mass, radius, height, and initial velocity of the object can be adjusted, as can the air density and wind.5 Minute Preview
Try to get a hole in one by adjusting the velocity and launch angle of a golf ball. Explore the physics of projectile motion in a frictional or ideal setting. Horizontal and vertical velocity vectors can be displayed, as well as the path of the ball. The height of the golfer and the force of gravity are also adjustable.5 Minute Preview
PI.2.2: : Describe the slope of the graphical representation of velocity vs. clock reading (time) in terms of the acceleration of the object.
Distance-Time and Velocity-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.5 Minute Preview
PI.2.3:排名对象在一个年代的加速度ystem based on the slope of a velocity vs. clock reading (time) graphical representation. Recognize that the magnitude of the slope representing a negative acceleration can be greater than the magnitude of the slope representing a positive acceleration.
Distance-Time and Velocity-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.5 Minute Preview
PI.2.4: : Given a graphical representation of the position, velocity, or acceleration vs. clock reading (time), be able to identify or sketch the shape of the other two graphs.
Free-Fall Laboratory
Investigate the motion of an object as it falls to the ground. A variety of objects can be compared, and their motion can be observed in a vacuum, in normal air, and in denser air. The position, velocity, and acceleration are measured over time, and the forces on the object can be displayed. Using the manual settings, the mass, radius, height, and initial velocity of the object can be adjusted, as can the air density and wind.5 Minute Preview
PI.2.5: : Qualitatively and quantitatively apply the models of constant velocity and constant acceleration to determine the position or velocity of an object moving in free fall near the surface of the Earth.
Feed the Monkey (Projectile Motion)
Fire a banana cannon at a monkey in a tree. The monkey drops from the tree at the moment the banana is fired from the cannon. Determine where to aim the cannon so the monkey catches the banana. The position of the cannon, launch angle and initial velocity of the banana can be varied. Students can observe the velocity vectors and the paths of the monkey and banana.5 Minute Preview
Investigate the motion of an object as it falls to the ground. A variety of objects can be compared, and their motion can be observed in a vacuum, in normal air, and in denser air. The position, velocity, and acceleration are measured over time, and the forces on the object can be displayed. Using the manual settings, the mass, radius, height, and initial velocity of the object can be adjusted, as can the air density and wind.5 Minute Preview
Try to get a hole in one by adjusting the velocity and launch angle of a golf ball. Explore the physics of projectile motion in a frictional or ideal setting. Horizontal and vertical velocity vectors can be displayed, as well as the path of the ball. The height of the golfer and the force of gravity are also adjustable.5 Minute Preview
PI.3.1: : Understand Newton’s first law of motion and describe the motion of an object in the absence of a net external force according to Newton’s first law.
Fan Cart Physics
Gain an understanding of Newton's Laws by experimenting with a cart (on which up to three fans are placed) on a linear track. The cart has a mass, as does each fan. The fans exert a constant force when switched on, and the direction of the fans can be altered as the position, velocity, and acceleration of the cart are measured.5 Minute Preview
PI.3.2: : Develop graphical and mathematical representations that describe the relationship among the inertial mass of an object, the total force applied, and the acceleration of an object in one dimension where one or more forces is applied to the object and apply those representations to qualitatively and quantitatively describe how a net external force changes the motion of an object.
Atwood Machine
Measure the height and velocity of two objects connected by a massless rope over a pulley. Observe the forces acting on each mass throughout the simulation. Calculate the acceleration of the objects, and relate these calculations to Newton's Laws of Motion. The mass of each object can be manipulated, as well as the mass and radius of the pulley.5 Minute Preview
Gain an understanding of Newton's Laws by experimenting with a cart (on which up to three fans are placed) on a linear track. The cart has a mass, as does each fan. The fans exert a constant force when switched on, and the direction of the fans can be altered as the position, velocity, and acceleration of the cart are measured.5 Minute Preview
Investigate the motion of an object as it falls to the ground. A variety of objects can be compared, and their motion can be observed in a vacuum, in normal air, and in denser air. The position, velocity, and acceleration are measured over time, and the forces on the object can be displayed. Using the manual settings, the mass, radius, height, and initial velocity of the object can be adjusted, as can the air density and wind.5 Minute Preview
PI.3.4: : Understand Newton’s third law of motion and describe the interaction of two objects using Newton’s third law and the representation of action-reaction pairs of forces.
Fan Cart Physics
Gain an understanding of Newton's Laws by experimenting with a cart (on which up to three fans are placed) on a linear track. The cart has a mass, as does each fan. The fans exert a constant force when switched on, and the direction of the fans can be altered as the position, velocity, and acceleration of the cart are measured.5 Minute Preview
PI.3.7: : Explain that the equivalence of the inertial and gravitational masses leads to the observation that acceleration in free fall is independent of an object’s mass.
Free-Fall Laboratory
Investigate the motion of an object as it falls to the ground. A variety of objects can be compared, and their motion can be observed in a vacuum, in normal air, and in denser air. The position, velocity, and acceleration are measured over time, and the forces on the object can be displayed. Using the manual settings, the mass, radius, height, and initial velocity of the object can be adjusted, as can the air density and wind.5 Minute Preview
PI.4.1: : Evaluate the translational kinetic, gravitational potential, and elastic potential energies in simple situations using the mathematical definitions of these quantities and mathematically relate the initial and final values of the translational kinetic, gravitational potential, and elastic potential energies in the absence of a net external force.
Energy of a Pendulum
Perform experiments with a pendulum to gain an understanding of energy conservation in simple harmonic motion. The mass, length, and gravitational acceleration of the pendulum can be adjusted, as well as the initial angle. The potential energy, kinetic energy, and total energy of the oscillating pendulum can be displayed on a table, bar chart or graph.5 Minute Preview
Investigate the energy and motion of a block sliding down an inclined plane, with or without friction. The ramp angle can be varied and a variety of materials for the block and ramp can be used. Potential and kinetic energy are reported as the block slides down the ramp. Two experiments can be run simultaneously to compare results as factors are varied.5 Minute Preview
Compare the potential energy of several objects when you place them on shelves of different heights. Learn that two objects at different heights can have the same potential energy, while two objects at the same height can have different potential energies.5 Minute Preview
Adjust the hills on a toy-car roller coaster and watch what happens as the car careens toward an egg (that can be broken) at the end of the track. The heights of three hills can be manipulated, along with the mass of the car and the friction of the track. A graph of various variables of motion can be viewed as the car travels, including position, speed, acceleration, potential energy, kinetic energy, and total energy.5 Minute Preview
PI.4.2: : Identify the forms of energy present in a scenario and recognize that the potential energy associated with a system of objects and is not stored in the object itself.
Energy of a Pendulum
Perform experiments with a pendulum to gain an understanding of energy conservation in simple harmonic motion. The mass, length, and gravitational acceleration of the pendulum can be adjusted, as well as the initial angle. The potential energy, kinetic energy, and total energy of the oscillating pendulum can be displayed on a table, bar chart or graph.5 Minute Preview
Investigate the energy and motion of a block sliding down an inclined plane, with or without friction. The ramp angle can be varied and a variety of materials for the block and ramp can be used. Potential and kinetic energy are reported as the block slides down the ramp. Two experiments can be run simultaneously to compare results as factors are varied.5 Minute Preview
Adjust the hills on a toy-car roller coaster and watch what happens as the car careens toward an egg (that can be broken) at the end of the track. The heights of three hills can be manipulated, along with the mass of the car and the friction of the track. A graph of various variables of motion can be viewed as the car travels, including position, speed, acceleration, potential energy, kinetic energy, and total energy.5 Minute Preview
PI.4.3: : Conceptually define “work” as the process of transferring of energy into or out of a system when an object is moved under the application of an external force and operationally define “work” as the area under a force vs. change in position curve.
Pulley Lab
Use a pulley system to lift a heavy weight to a certain height. Measure the force required to lift the weight using up to three fixed and three movable pulleys. The weight to be lifted and the efficiency of the pulley system can be adjusted, and the height of the weight and the total input distance are reported.5 Minute Preview
PI.4.4: : For a force exerted in one or two dimensions, mathematically determine the amount of work done on a system by an unbalanced force over a change in position in one dimension.
Inclined Plane - Simple Machine
Investigate how an inclined plane redirects and reduces the force pulling a brick downward, with or without friction. A toy car can apply a variable upward force on the brick, and the mechanical advantage and efficiency of the plane can be determined. A graph of force versus distance illustrates the concept of work.5 Minute Preview
PI.4.5: : Understand and apply the principle of conservation of energy to determine the total mechanical energy stored in a closed system and mathematically show that the total mechanical energy of the system remains constant as long as no dissipative (i.e. nonconservative) forces are present.
Air Track
Adjust the mass and velocity of two gliders on a frictionless air track. Measure the velocity, momentum, and kinetic energy of each glider as they approach each other and collide. Collisions can be elastic or inelastic.5 Minute Preview
A falling cylinder is attached to a rotating propeller that stirs and heats the water in a beaker. The mass and height of the cylinder, as well as the quantity and initial temperature of water can be adjusted. The temperature of the water is measured as energy is converted from one form to another.5 Minute Preview
Investigate the energy and motion of a block sliding down an inclined plane, with or without friction. The ramp angle can be varied and a variety of materials for the block and ramp can be used. Potential and kinetic energy are reported as the block slides down the ramp. Two experiments can be run simultaneously to compare results as factors are varied.5 Minute Preview
PI.4.6: : Develop and apply pictorial, mathematical or graphical representations to qualitatively and quantitatively predict changes in the mechanical energy (e.g. translational kinetic, gravitational, or elastic potential) of a system due to changes in position or speed of objects or non-conservative interactions within the system.
Inclined Plane - Sliding Objects
Investigate the energy and motion of a block sliding down an inclined plane, with or without friction. The ramp angle can be varied and a variety of materials for the block and ramp can be used. Potential and kinetic energy are reported as the block slides down the ramp. Two experiments can be run simultaneously to compare results as factors are varied.5 Minute Preview
PI.5.1: : For an object moving at constant rate, define linear momentum as the product of an object’s mass and its velocity and be able to quantitatively determine the linear momentum of a single object.
2D Collisions
Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios.5 Minute Preview
Adjust the mass and velocity of two gliders on a frictionless air track. Measure the velocity, momentum, and kinetic energy of each glider as they approach each other and collide. Collisions can be elastic or inelastic.5 Minute Preview
PI.5.3: : Demonstrate that when two objects interact through a collision or separation that both the force experienced by each object and change in linear momentum of each object are equal and opposite, and as the mass of an object increases, the change in velocity of that object decreases.
2D Collisions
Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios.5 Minute Preview
Adjust the mass and velocity of two gliders on a frictionless air track. Measure the velocity, momentum, and kinetic energy of each glider as they approach each other and collide. Collisions can be elastic or inelastic.5 Minute Preview
PI.5.4: : Determine the individual and total linear momentum for a two-body system before and after an interaction (e.g. collision or separation) between the two objects and show that the total linear momentum of the system remains constant when no external force is applied consistent with Newton’s third law.
2D Collisions
Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios.5 Minute Preview
Adjust the mass and velocity of two gliders on a frictionless air track. Measure the velocity, momentum, and kinetic energy of each glider as they approach each other and collide. Collisions can be elastic or inelastic.5 Minute Preview
PI.5.5: : Classify an interaction (e.g. collision or separation) between two objects as elastic or inelastic based on the change in linear kinetic energy of the system.
2D Collisions
Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios.5 Minute Preview
Adjust the mass and velocity of two gliders on a frictionless air track. Measure the velocity, momentum, and kinetic energy of each glider as they approach each other and collide. Collisions can be elastic or inelastic.5 Minute Preview
PI.5.6: : Mathematically determine the center of mass of a system consisting of two or more masses. Given a system with no external forces applied, show that the linear momentum of the center of mass remains constant during any interaction between the masses.
2D Collisions
Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios.5 Minute Preview
PI.6.1: : Develop graphical and mathematical representations that describe the relationship between the amount of stretch of a spring and the restoring force and apply those representations to qualitatively and quantitatively describe how changing the stretch or compression will affect the restoring force and vice versa, specifically for an ideal spring.
Determining a Spring Constant
Place a pan on the end of a hanging spring. Measure how much the spring stretches when various masses are added to the pan. Create a graph of displacement vs. mass to determine the spring constant of the spring.5 Minute Preview
PI.6.2:描述图形repr的斜率esentation of restoring force vs. change in length of an elastic material in terms of the elastic constant of the material, specifically for an ideal spring.
Determining a Spring Constant
Place a pan on the end of a hanging spring. Measure how much the spring stretches when various masses are added to the pan. Create a graph of displacement vs. mass to determine the spring constant of the spring.5 Minute Preview
PI.6.4: : Develop graphical and mathematical representations which describe the relationship between the strength of gravity, length of string, and period of a simple mass-string (i.e. pendulum) system apply the those representations to qualitatively and quantitatively describe how changing the length of string or strength of gravity will affect the period of the system in the limit of small amplitudes.
Period of a Pendulum
Practice measuring the period of a pendulum. Perform experiments to determine how mass, length, gravitational acceleration, and angle affect the period of a pendulum.5 Minute Preview
PI.7.1: : Differentiate between transverse and longitudinal modes of oscillation for a mechanical wave traveling in one dimension.
Longitudinal Waves
Observe the propagation of longitudinal (compression) waves in a closed or open tube with evenly-spaced dividers. The strength and frequency of the waves can be manipulated, or waves can be observed as individual pulses. Compare the movement of dividers to graphs of displacement, velocity, acceleration and pressure.5 Minute Preview
PI.7.2: : Understand that a mechanical wave requires a medium to transfer energy, unlike an electromagnetic wave, and that only the energy is transferred by the mechanical wave, not the mass of the medium.
Longitudinal Waves
Observe the propagation of longitudinal (compression) waves in a closed or open tube with evenly-spaced dividers. The strength and frequency of the waves can be manipulated, or waves can be observed as individual pulses. Compare the movement of dividers to graphs of displacement, velocity, acceleration and pressure.5 Minute Preview
PI.7.5: : Apply the mechanical wave model to sound waves and qualitatively and quantitatively determine how the relative motion of a source and observer affects the frequency of a wave as described by the Doppler Effect.
Doppler Shift
Observe sound waves emitted from a moving vehicle. Measure the frequency of sound waves in front of and behind the vehicle as it moves, illustrating the Doppler effect. The frequency of sound waves, speed of the source, and the speed of sound can all be manipulated. Motion of the vehicle can be linear, oscillating, or circular.5 Minute Preview
Derive an equation to calculate the frequency of an oncoming sound source and a receding sound source. Also, calculate the Doppler shift that results from a moving observer and a stationary sound source. The source velocity, sound velocity, observer velocity, and sound frequency can all be manipulated.5 Minute Preview
PI.7.6: : Qualitatively and quantitatively apply the principle of superposition to describe the interaction of two mechanical waves or pulses.
Ripple Tank
Study wave motion, diffraction, interference, and refraction in a simulated ripple tank. A wide variety of scenarios can be chosen, including barriers with one or two gaps, multiple wave sources, reflecting barriers, or submerged rocks. The wavelength and strength of waves can be adjusted, as well as the amount of damping in the tank.5 Minute Preview
Listen to and see interference patterns produced by sound waves with similar frequencies. Test your ability to distinguish and match sounds as musicians do when they tune their instruments. Calculate the number of "sound beats" you will hear based on the frequency of each sound. [Note: Headphones are recommended for this Gizmo.]5 Minute Preview
PI.7.7: : Qualitatively describe the phenomena of both resonance frequencies and beat frequencies that arise from the interference of sound waves of slightly different frequency and define the beat frequency as the difference between the frequencies of two individual sound wave sources.
Longitudinal Waves
Observe the propagation of longitudinal (compression) waves in a closed or open tube with evenly-spaced dividers. The strength and frequency of the waves can be manipulated, or waves can be observed as individual pulses. Compare the movement of dividers to graphs of displacement, velocity, acceleration and pressure.5 Minute Preview
PI.8.1:开发图形、数学和照片torial representations that describe the relationship between length, cross-sectional area, and resistivity of an ohmic device and apply those representations to qualitatively and quantitatively describe how changing the composition, size, or shape of the device affect the resistance.
Circuit Builder
Create circuits using batteries, light bulbs, switches, fuses, and a variety of materials. Examine series and parallel circuits, conductors and insulators, and the effects of battery voltage. Thousands of different circuits can be built with this Gizmo.5 Minute Preview
PI.8.5: : Qualitatively and quantitatively describe how changing the voltage or resistance of a simple series (i.e. loop) circuit affects the voltage, current, and power measurements of individual resistive devices and for the entire circuit.
Advanced Circuits
Build compound circuits with series and parallel elements. Calculate voltages, resistance, and current across each component using Ohm's law and the equivalent resistance equation. Check your answers using a voltmeter, ammeter, and ohmmeter. Learn the function of fuses as a safety device.5 Minute Preview
Create circuits using batteries, light bulbs, switches, fuses, and a variety of materials. Examine series and parallel circuits, conductors and insulators, and the effects of battery voltage. Thousands of different circuits can be built with this Gizmo.5 Minute Preview
Build electrical circuits using batteries, light bulbs, resistors, fuses, wires, and a switch. An ammeter, a voltmeter and an ohmmeter are available for measuring current, voltage and resistance throughout the circuit. The voltage of the battery and the precision of the meters can be adjusted. Multiple circuits can be built for comparison.5 Minute Preview
PI.8.6::定性和定量堤防e how changing the voltage or resistance of a simple parallel (i.e. ladder) circuit affects the voltage, current, and power measurements of individual resistive devices and for the entire circuit.
Advanced Circuits
Build compound circuits with series and parallel elements. Calculate voltages, resistance, and current across each component using Ohm's law and the equivalent resistance equation. Check your answers using a voltmeter, ammeter, and ohmmeter. Learn the function of fuses as a safety device.5 Minute Preview
Create circuits using batteries, light bulbs, switches, fuses, and a variety of materials. Examine series and parallel circuits, conductors and insulators, and the effects of battery voltage. Thousands of different circuits can be built with this Gizmo.5 Minute Preview
Build electrical circuits using batteries, light bulbs, resistors, fuses, wires, and a switch. An ammeter, a voltmeter and an ohmmeter are available for measuring current, voltage and resistance throughout the circuit. The voltage of the battery and the precision of the meters can be adjusted. Multiple circuits can be built for comparison.5 Minute Preview
PI.8.9: : Use a description or schematic diagram of an electrical circuit to calculate unknown values of current, voltage, or resistance in various components or branches of the circuit according to Ohm’s Law, Kirchhoff’s junction rule, and Kirchhoff’s loop rule.
Advanced Circuits
Build compound circuits with series and parallel elements. Calculate voltages, resistance, and current across each component using Ohm's law and the equivalent resistance equation. Check your answers using a voltmeter, ammeter, and ohmmeter. Learn the function of fuses as a safety device.5 Minute Preview
Create circuits using batteries, light bulbs, switches, fuses, and a variety of materials. Examine series and parallel circuits, conductors and insulators, and the effects of battery voltage. Thousands of different circuits can be built with this Gizmo.5 Minute Preview
Build electrical circuits using batteries, light bulbs, resistors, fuses, wires, and a switch. An ammeter, a voltmeter and an ohmmeter are available for measuring current, voltage and resistance throughout the circuit. The voltage of the battery and the precision of the meters can be adjusted. Multiple circuits can be built for comparison.5 Minute Preview
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
