Energy transfers for AQA A-level Physics
This page covers the following topics:
2. Force-displacement graphs
3. Conservation of energy
Work done is calculated by multiplying the horizontal component of the force being exerted on an object and the distance through which it is moved, where the distance moved by the object is in the direction parallel to the direction of the force. When the force F is not along the line of motion, but instead at an angle θ to it, the relevant force component can be calculated using Fcos(θ).
A force-displacement graph shows how the force exerted by an object changes as its displacement changes. The area under a force-displacement graph is the work done by the object. For non-linear graphs, the area under a force-displacement graph can be approximated by the area of small squares.
The principle of conservation of energy states that in a closed system, the total energy before an energy change is equal to the total energy after. In other words, the total energy in a closed system is constant. This means that energy cannot be destroyed nor created.
A mechanical lift is being used to lift up an object of 4.5 kg. Given that the work done by the lift is 600 J and that there are no frictional forces, calculate the height through which the box is lifted.
By the principle of conservation of energy, the total energy remains constant.
GPE = W
mgh = Fd
4.5 kg × h × 9.8 = 600
h = 13.6 m (to 3 sf)
Sketch a force-displacement graph for an object moving at a constant force of 15 N for 7 m and then constantly decreasing its force to 0 for the next 5 m.
The object moves at a constant force of 15 N for 7 m and then constantly decreases its force to 0 for the next 5 m.
Describe, using the principle of conservation of energy, the energy changes that occur when a ball is rolled down a hill.
At the top of the hill, the ball will possess gravitational potential energy. As the ball starts moving this will be transferred into kinetic energy. Some of the energy will also be transferred into heat energy, since the temperature of the ball will rise, as work is done against the frictional forces. By the principle of conservation of energy, the sum of the kinetic energy and the heat energy will be equal to the gravitational potential energy.
gravitational potential energy = kinetic energy + heat energy
On the given force-displacement graph, the motion of two cars is being described by the two lines. Calculate the difference in the work done by the two cars.
The area under the graph is the work done by each car.
For car A, work done = 0.5 × 80 × (100 + 150) = 10000 J.
For car B, work done = 0.5 × 80 × (125 − 40 + 150) = 9400 J.
difference = 10000 J − 9400 J = 600 J
A car is moving down a slope of 20° to the horizontal. Given that the horizontal thrust exerted by the car is 1600 N, calculate the work done by the car when it is moved through a distance of 7 m down the slope.
W = Fcos(θ) × d
W = 1600cos(20°) × 7 = 10524.56 J (to 2 decimal places)
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