1 A grandfather clock uses energy stored in raised weights. The weights transfer energy to the clock mechanism as they fall. One clock has a 4.5 kg weight that supplies energy to the chimes (which play a few notes every 15 minutes), and two 3.5 kg weights that power the clock and the mechanism that strikes the hours.
For all questions on this sheet,
use g = 10 N/kg
a Calculate how much energy is stored when all three of these weights are raised by 70 cm. b How far does the 4.5 kg weight have to be lifted to store 45 J of energy?
2 The water tank in a house can hold 200 litres of water. The mass of 1 litre of water is 1 kg. The tank is 2 m above the bathroom taps and 5 m above the kitchen taps. The kitchen taps are 1 m above the floor.
a
Calculate the gravitational potential energy (GPE stored in the water in the tank when it is full. State any assumptions made in your answer.
b Calculate the speed at which the water would come out of the bathroom taps and kitchen taps. You
may assume that no energy is transferred due to friction in the pipes.
3 The Victoria Falls in Africa is one of the world's largest waterfalls. Just over 1000 m° of water pass over the falls every second and fall approximately 100 m. 1 m3 of water has a mass of 1000 kg. a What mass of water goes over the falls every second? Give your answer in standard form.
b
Calculate the GPE of 1 kg of water at the top of the falls.
c If all the GPE stored in 1 kg of water is transferred to kinetic energy, calculate the speed of the water as
it reaches the bottom.
d Suggest why the water will not be falling as fast as your answer to part c suggests. e What is the total energy transferred per second as the GP stored in the water falling in one second is
transferred to other energy stores.
f Suggest the ways in which this energy is finally stored.
4 A post driver is used to drive fence posts into the ground. It is a hollow tube with a closed top, and handles on the side. A person fits the driver over a fence post, then lifts it up and lets it drop.
post driver
50 cm
a A post driver has a mass of 10 kg. Calculate the change in GPE stored when the post driver is lifted by 50 cm above the post, as shown in the diagram.
b
Calculate the speed of the driver when the end hits the post.
C
Explain how much extra energy is stored if the post driver is
fence post
lifted by 1 metre instead of only 50 cm.
d Calculate the speed of the post driver after it falls for 1 m. e A new design of post driver has a mass of 15 kg. Suggest one advantage and one disadvantage of this new design.
Extra challenge
5 F The post driver in question 4a stops in
0.5 seconds when it hits the fence post.
a Calculate the force needed to bring the post driver to a stop. (Hint: use your answer to 4b.)
The momentum of a moving object is the product of its mass and its velocity. The force needed to stop a moving object depends on how fast its momentum changes.
force = change in momentum
=
mv - mu
time
t
b What provides this force?
c Explain how your answer might be different it the post were being sunk into very soft ground,
F = force (N)
u = initial velocity (m/s)
te time (s)
m = mass (kg)
v = final velocity (m/s)