Power

A student places a trolley at the top of a runway, as shown in Figure 9.

The student had to lift the trolley through a height of 26 cm to put it at the top of the runway.

The gravitational potential energy, Δ GPE, of the trolley increases by 4.1 J when lifted to the top of the runway.

The gravitational field strength, g, = 10 N / kg.

Show that the mass of the trolley is about 1.6 kg.

Use the equation

The student releases the trolley and the trolley moves down the runway.

The student assumes that all the extra gravitational potential energy, Δ GPE, stored at the top of the runway is transferred to kinetic energy at the end of the runway.

Calculate the expected value of the velocity of the trolley at the end of the runway.

Use the equation

expected velocity =_........

The light gate, shown in Figure 9, is used to determine the actual velocity of the trolley at the end of the runway.

The actual velocity at the end of the runway is less than the expected velocity as calculated in part (ii).

Suggest one way to reduce the difference between the actual velocity and the expected velocity.

A different student finds out how much power can be generated by running up some stairs in a measured amount of time.

The following quantities are measured:

mass of student = 48 kg

total height of stairs = 2.9 m

time to run up stairs = 3.4 s

Calculate the power the student generated.

Give the answer to 2 significant figures (2 s.f.).

Use the equation

Explain how the total height of the stairs can be found using a 50 cm ruler.

A student places a trolley at the top of a runway, as shown in Figure 1.

The student had to lift the trolley through a height of 26 cm to put it at the top of the runway.

The gravitational potential energy, Δ GPE, of the trolley increases by 4.1 J when lifted to the top of the runway.

The gravitational field strength, g, = 10 N / kg.

Show that the mass of the trolley is about 1.6 kg.

Use the equation

The student releases the trolley and the trolley moves down the runway.

The student assumes that all the extra gravitational potential energy, ∆ GPE, stored at the top of the runway is transferred to kinetic energy at the end of the runway.

Calculate the expected value of the velocity of the trolley at the end of the runway.

Use the equation

expected velocity =_........

The light gate, shown in Figure 1, is used to determine the actual velocity of the trolley at the end of the runway.

The actual velocity at the end of the runway is less than the expected velocity as calculated in (ii).

Suggest one way to reduce the difference between the actual velocity and the expected velocity.

A different student finds out how much power can be generated by running up some stairs in a measured amount of time.

The following quantities are measured:

mass of student = 48 kg

total height of stairs = 2.9 m

time to run up stairs = 3.4 s

Calculate the power the student generated.

Give the answer to 2 significant figures (2 s.f.).

Use the equation

Figure 5 shows a truck on a horizontal road.

A force of 1200 N pulls the truck along the road for a distance of 8.0 m.

Calculate the work done by the 1200 N force.

Use the equation

work done = force distance moved in the direction of the force

State the unit of work done.

work done =_........

unit_........

At 8.0 m the force is removed and the truck slows down until it stops.

Describe the energy transfers as the truck slows down.

A box has a mass of 90 kg.

Which of these is the weight of the box?

Figure 6 shows a truck lifting a different box.

A student calculates the change in gravitational potential energy, ΔGPE, for the box at different heights.

Figure 7 shows the results of the student’s calculations.

The student has made one incorrect calculation.

The truck lifts the box from the ground to a height of 2.0 m.

This takes a time of 5.0 s.

Using data from the graph in Figure 7, calculate the power needed to lift the box.

Use the equation

power =_........ W

Figure 8 shows a saucepan of milk being heated on an electric cooker.

Figure 8

Figure 9 is a table of data about the milk being heated.

Using data from the table in Figure 9, calculate the increase in temperature of the milk.

increase in temperature =_........ °C

Using data from the table in Figure 9, calculate the specific heat capacity of the milk.

Use the equation

specific heat capacity =_........ J/kg °C

The cooker supplies 130 000 J of energy in a time of 87 s.

Calculate the power supplied by the cooker.

Use the equation

Give your answer to 2 significant figures.

power =_........ W

The cooker supplies 130 000 J of energy but only 96 000 J of this energy is used to heat the milk.

Calculate the efficiency of heating the milk using this cooker.

Use the equation

efficiency =_........

The wiring for the cooker has safety features.

Which of these wires would help to protect a person from getting an electric shock if a fault developed in the cooker?

Explain how a fuse can prevent overheating of the wiring for the cooker.

Three students carry out an investigation to determine their powers when running up stairs.

Figure 7 shows a diagram of the stairs with four distances, A, B, C and D, marked.

The students need to calculate the work done against gravity.

Which distance should be used in the calculation?

They take turns to run up the stairs and use a stopwatch to measure the time taken.

The students estimate their own weight.

Figure 8 shows a table of their results.

The table is not complete.

State the unit for work done.

unit for work done is_........

Use the data for student B to calculate his estimated weight.

weight =_........ N

Use the data for student C to calculate the time she takes.

time taken =_........ s

Use the data for all three students to calculate the average power of the students.

average power =_........ W

Identify a significant source of error in the investigation and state how this error can be reduced.

source of error

can be reduced by

Calculate the change in gravitational potential energy of the rover as it descends from position P to position Q.

Mass of rover = 1100 kg

Gravitational field strength on Mars = 3.7 N / kg

Give your answer to 2 significant figures.

change in gravitational potential energy =_........ J

Use data from Figure 6 to calculate the change in kinetic energy of the rover as it descends from position P to position Q.

change in kinetic energy =_........ J

The rover is slowed down safely using thrusters and a parachute (not shown in Figure 6).

The thrusters use jets of gas to control movements and the parachute is designed to be used in the atmosphere of Mars.

Describe the energy changes involved in terms of the work done by various forces as the rover descends.

The rover uses solar panels for its power needs.

The solar panels can provide 1200 W of power.

Show that the solar panels can provide 2.16 MJ of energy in 30 minutes.

The solar panels convert 27% of the energy they receive from the Sun into electricity.

Calculate the solar energy received by the panels that provides the 2.16 MJ of energy.

energy received =_........ J

Figure 13 shows a drone.

The drone has four spinning blades.

The upward force produced enables the drone to rise in the air.

The speed at which the blades spin is measured in turns per minute.

Figure 14 shows how the upward force produced by the four blades depends on the speed at which the blades spin.

Describe the relationship between upward force and speed shown by this graph.

A different drone has a mass of 4.5 kg.

This drone rises from the ground to a height of 20 m.

Calculate the change in gravitational potential energy when the drone rises through a height of 20 m.

The gravitational field strength g = 10 N/kg.

change in gravitational potential energy =_........ J

State the amount of useful work done by the blades as the drone rises through 20 m.

useful work done =_........ J

It takes 4 s for the drone to rise through 20 m.

Calculate the useful power developed by the blades in this time of 4 s.

useful power developed =_........ W

*(c) The blades on the drone are turned by electric motors.

The electric motors are powered by a battery.

Figure 15 represents the energy transfers involved when the drone rises from the ground.

Describe the changes in the way energy is stored when the drone rises from the ground.

Your answer should refer to energy transfers.

Figure 4 shows a drone.

The drone has four spinning blades.

The upward force produced enables the drone to rise in the air.

The speed at which the blades spin is measured in turns per minute.

Figure 5 shows how the upward force produced by the four blades depends on the speed at which the blades spin.

Describe the relationship between upward force and speed shown by this graph.

A different drone has a mass of 4.5 kg.

This drone rises from the ground to a height of 20 m.

Calculate the change in gravitational potential energy when the drone rises through a height of 20 m.

The gravitational field strength g = 10 N/kg.

change in gravitational potential energy =_........ J

State the amount of useful work done by the blades as the drone rises through 20 m.

useful work done =_........ J

It takes 4 s for the drone to rise through 20 m.

Calculate the useful power developed by the blades in this time of 4 s.

useful power developed =_........ W

Figure 7 shows an athlete using a fitness device.

The athlete stretches the spring in the device by pulling the handles apart.

The spring constant of the spring is 140 N/m.

The athlete does 45 J of work to extend the spring.

The athlete takes 0.6 s to expand the spring.

Calculate the useful power output of the athlete when stretching the spring.

useful power output of the athlete =_........ W

Calculate the extension of the spring.

Use an equation selected from the list of equations at the end of this paper.

extension of the spring =_........ m

A student investigates the stretching of a long piece of rubber.

Figure 8 shows the apparatus to be used.

Figure 8

The student puts just enough weight on the weight hanger to make the piece of rubber just tight.

The student wants to plot a graph to show how the extension of the piece of rubber varies with the force used to stretch it.

The student adds a known weight to the weight hanger.

Describe how the student could measure the extension of the rubber when he adds another weight to the weight hanger.

The student obtains a series of values of force and extension while loading the piece of rubber and then unloading it.

Figure 9 shows the graph of the student’s values.

Explain how the shape of this graph shows that the distortion of the piece of rubber being stretched is different from the distortion of a spring being stretched.

The area between the curve and the extension axis of a force/extension graph corresponds to work done or energy transferred.

Suggest what the shaded area of the graph in Figure 9 represents.

A cyclist is riding a bicycle at a steady velocity of 12 m/s.

The cyclist and bicycle have a total mass of 68 kg.

Calculate the kinetic energy of the cyclist and bicycle.

Use the equation

kinetic energy =_........ J

Describe the energy transfers that happen when the cyclist uses the brakes to stop.

The cyclist starts to cycle again.

The cyclist does 1600 J of useful work to travel 28 m.

Calculate the average force the cyclist exerts.

average force =_........ N

*(d) A class of students investigate the power output of each student in the class.

The class must decide whether they use a method using steps or a method using weights. The whole class must use the same method.

Plan what measurements the students should take and how these can be used to calculate and compare the power output of each student.

You may draw a diagram to help with your plan.

A cyclist is riding a bicycle at a steady velocity of 12 m/s.

The cyclist and bicycle have a total mass of 68 kg.

Calculate the kinetic energy of the cyclist and bicycle.

Use the equation

kinetic energy =_........ J

Describe the energy transfers that happen when the cyclist uses the brakes to stop.

The cyclist starts to cycle again.

The cyclist does 1600 J of useful work to travel 28 m.

Calculate the average force the cyclist exerts.

average force =_........ N

An athlete uses a training machine in a gym.

The display on the machine shows the time spent on the machine and the amount of energy transferred during a training session.

Figure 3 shows the displays for two different sessions by the same athlete.

Explain what the displays show about the average power of the athlete in each of these two sessions.

Figure 5 shows the vertical forces on an aeroplane.

Use information from the diagram to determine the size and direction of the resultant vertical force on the aeroplane.

size =_........ kN, direction is_........

The aeroplane is descending.

Figure 6 shows a diagram of the resultant vertical and horizontal forces on the aeroplane as it is descending.

Complete the diagram to show the resultant of these two forces.

The mass of the aeroplane is 750 kg.

Calculate the change in gravitational potential energy of the aeroplane as it descends from 1300 m to the ground.

Gravitational field strength (g) = 10 N/kg

energy =_........ J

The aeroplane is powered by an engine that burns fuel.

The fuel supplies a total of 6500 kJ of energy every minute.

The efficiency of the engine is 0.70 (70%).

Calculate the power output of the engine.

Give your answer in kW.

power =_........ kW

Explain why the efficiency of the engine is less than 1 (100%).