Energy Problem Set.
In order to move a very heavy crate (mass = 500 kg) across a bitumen surface, Susan decides to use her landcruiser. She positions the bulbar against the crate and pushes it across the bitumen.
The bitumen surface applies a maximum uniform frictional force of 2500 N throughout the slide.
The crate started from rest, sliding with uniform acceleration, a distance of 15 m in 10 seconds.
The land cruiser stops pushing the crate at the end of the 10 second period, mentioned above.
The crate, which is currently moving at 3 ms-1 is quickly brought to rest by the frictional force.
1. How much kinetic energy did the crate possess at the instant the landcruiser stopped pushing? [2]
2. How much work was done on the crate by the frictional force to stop it? [2]
3. Explain what happened to the energy possessed by the crate from the moment
the truck stopped pushing until the crate came to rest. [2]
The crate took 0.6 seconds to come to rest.
4. Calculate the rate at which the energy of the crate is converted as it comes to rest. [2]
5. Determine the total distance travelled by the crate from the moment it was pushed until it came
to rest. Show your working. [3]
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Phillip is testing his nerve and skills on the new 8 metre high half pipe - ‘Thrillseeker’. Phillip starts from rest by stepping off the lip of the half pipe, 8 metres above the bottom and rolls down into the half-pipe.
Phillip has a mass of 60 kg. Take g = 10 ms-2
6. Determine Phillip’s speed at point X of the half pipe, assuming negligible energy losses to friction. [2]
7. Calculate the speed Phillip possesses when he is at position Y in the half pipe. [2]
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A skier of total mass 80 kg is initially travelling at 2.0 ms-1 when she begins her descent down a smooth slope of an 18 m high hill. At no time does she use her arms or poles to provide extra force during the descent. Take g = 10 N/kg in all relevant areas.
8. Determine the value of the kinetic energy of the skier before she begins her hill descent. [1]
9. Calculate how much gravitational potential energy she possesses while still on top of the hill. [1]
10. What will be the speed of the skier at the bottom of the hill if (drag) friction effects are negligible? [2]
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Pat (a Year 6 student) decides to roll down the incline towards the pizza hut in her go-kart. Pat starts rolling with an initial speed of 0.5 ms-1 and travels through a vertical height of 4.2 m. Her speed at the bottom of the incline is measured at 6.5 ms-1. The mass of Pat and the go-kart is 60 kg; take g = 10 Nkg-1.
11. Determine how much energy is ‘lost’ during Pat descent in the go-kart. [2]
12. Explain where this ‘lost’ energy has gone and why it is considered ‘lost’. [1+1]
13. Calculate the rate of energy transformation/transfer if the descent took 1/2 minute. [2]
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Testing of a car’s braking system requires an 800 kg car to travel at V ms-1, then brake to rest without skidding. Computer equipment measures the size of the force acting on the car (friction) and the distance travelled from the moment that the brakes are applied until the car is stationary.
14. Calculate the work done by the brakes on the car in order to bring it to rest. [2]
15. Determine the time rate of energy dissipation during the braking period of 5.0 seconds. [2]
16. If all of the kinetic energy of the car was converted into heat and sound energy, deduce the
value of this kinetic energy that the car possessed just prior to commencing to brake. [2]
17. Deduce the value of V, the speed of the car, just prior to the commencement of braking. [2]
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A cart on a roller coaster rolls down a track as shown below. The upper section of the track is straight and the lower section forms part of a circle. The cart freely and smoothly rolls along the length of track.
The mass of the cart is 200 kg.
18. On the sketch above, clearly label the forces of N and W (weight) acting on the cart at X. [2]
19. On the sketch above, clearly label the forces of N and W (weight) acting on the cart at Y. [2]
20. What is the value of gravitational potential energy possessed by the cart at X?
Assume the value of gravitational potential energy possessed by the cart at Y = 0. [2]
21. How much energy does the cart possess when at the position labelled, ‘end of the ride’? [2]
22. Determine the speed of the cart at X. Show your working. [3]
23. How much kinetic energy does the cart possess when at position Y? [2]
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