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The work-energy
theorem
Objectives
- Investigate quantities using the work-energy theorem in various situations.
- Calculate quantities using the work-energy theorem in various situations.
- Design and implement an investigation: make observations, ask questions, formulate testable hypotheses, identify variables, select appropriate equipment, and evaluate answers.
Assessment
- If 20 joules of positive net work is done on an object then... A. the kinetic energy of the object remains the same. B. the kinetic energy of the object increases by 20 joules. C. the kinetic energy of the object decreases by 20 joules. D. the kinetic energy of the object must equal 20 joules.
Assessment
- A spring does 30 J of net work to accelerate a 5.0 kg mass from rest. What is the resulting speed of the mass?
- A 1,600 kg car traveling 30 m/s puts on brakes that apply a force equal to 1/2 the weight of the car. How far does the car travel before coming to a stop once the brakes are applied?
Physics terms
Equations
The work-energy theorem: The total work done on an object equals its change in kinetic energy.
or
The work-energy theorem Newton’s second law is a fundamental statement that relates the net force on an object to its acceleration. The work-energy theorem Newton’s second law is a fundamental statement that relates the net force on an object to its acceleration. The work-energy theorem is a fundamental statement that relates the net work—work done by the net force— to changes in an object’s energy. The work-energy theorem What is this equation telling us? Let’s write it out in more detail: It tells us that when a net force does work on an object, then the object speeds up or slows down. Work is zero if Fnet is zero A box is at rest on a frictionless table top. The force of gravity and the normal force from the table do zero work on the box. The net work is zero, so the box does not gain or lose kinetic energy. That makes sense! Positive work If you apply a horizontal force to the box, it will speed up in the direction of the force. Positive work is done on the box, and it gains kinetic energy. Force Negative work If you apply a force to slow down the box, you do negative work on the box. Negative work is done on the box, and it loses kinetic energy.
Finding the speed 10 kg A 10 kg box is initially at rest. A 50 N net force is applied to the box for a distance of 5.0 meters. What is the resulting speed of the box?
50 N
5 m Check your units 10 kg 50 N It’s always smart to check the units. 5 m Another example vi The distance it takes for a car to come to a complete stop can also be determined using the work-energy theorem. Stopping distance A car traveling at 25 m/s skids to a stop. The coefficient of friction is 0.80 between the tires and the road. What force is doing work to stop the car? vi Stopping distance A car traveling at 25 m/s skids to a stop. The coefficient of friction is 0.80 between the tires and the road. What force is doing work to stop the car? Friction provides the net force. It does negative work on the car. vi Stopping distance A car traveling at 25 m/s skids to a stop. The coefficient of friction is 0.80 between the tires and the road. How far does the car skid? vi
Stopping distance A car traveling at 25 m/s skids to a stop. The coefficient of friction is 0.80 between the tires and the road. How far does the car skid? vi Stopping distance A car traveling at 25 m/s skids to a stop. The coefficient of friction is 0.80 between the tires and the road. How far does the car skid? vi Stopping distance A car traveling at 25 m/s skids to a stop. The coefficient of friction is 0.80 between the tires and the road. How far does the car skid? vi Stopping distance A car traveling at 25 m/s skids to a stop. The coefficient of friction is 0.80 between the tires and the road. How far does the car skid? vi Stopping distance If the car is replaced with a massive truck, how much farther will it skid? vi Examine this equation for stopping distance: Stopping distance If the car is replaced with a massive truck, how much farther will it skid? the same distance If the car is moving twice as fast, how much farther does it skid? Examine this equation for stopping distance: vi
How much work does the rubber band do on the plane? Work done by the rubber band To get the answer we need the graph of force vs. distance. Work done by the rubber band What is the work done by a force of 6 N acting for 6 cm? Review: force vs. distance graph What is the work done by a force of 6 N acting for 6 cm? Review: force vs. distance graph What is the work done by a force of 6 N acting for 6 cm? The work done by a force It equals the area of this rectangle on the graph. 6 N x 0.06 m = 0.36 J Work done by a rubber band Measure and graph the force of the rubber band at different distances.
The work is the area of these shapes on the graph. Measure and graph the force of the rubber band at different distances. Work done by a rubber band The speed of the plane depends on the work done by the rubber band. The model The model The speed of the plane depends on the work done by the rubber band. The model The speed of the plane depends on the work done by the rubber band. The speed of the plane depends on the work done by the rubber band. The kinetic energy of the plane can’t be greater than the net work done by the rubber band... so this is the plane’s maximum possible velocity. The model Construct the paper airplane: step 1
Compare the launched kinetic energy with the work done by the rubber band. Calculate the efficiency: Determine the efficiency Assessment
- If 20 joules of positive net work is done on an object then... A. the kinetic energy of the object remains the same. B. the kinetic energy of the object increases by 20 joules. C. the kinetic energy of the object decreases by 20 joules. D. the kinetic energy of the object must equal 20 joules. Assessment
- If 20 joules of positive net work is done on an object then... A. the kinetic energy of the object remains the same. B. the kinetic energy of the object increases by 20 joules. C. the kinetic energy of the object decreases by 20 joules. D. the kinetic energy of the object must equal 20 joules. For example: if its initial kinetic energy was 10 joules, then its new kinetic energy is 30 joules. Assessment
- A spring does 30 J of net work to accelerate a 5.0 kg mass from rest. What is the resulting speed of the mass? Assessment
- A spring does 30 J of net work to accelerate a 5.0 kg mass from rest. What is the resulting speed of the mass? Assessment
- A 1,600 kg car traveling 30 m/s puts on brakes that apply a force equal to 1/2 the weight of the car. How far does the car travel before coming to a stop once the brakes are applied?
The force applied is one half of the car’s weight or: The total work done is equal to the change in the car’s kinetic energy: Solve for the distance: Assessment
- A 1,600 kg car traveling 30 m/s puts on brakes that apply a force equal to 1/2 the weight of the car. How far does the car travel before coming to a stop once the brakes are applied?
