Gravitational Potential Energy & Kinetic Energy
acceleration due to gravity = 9.81 ms-2
1. A car has a mass of 750 kg. Calculate its kinetic energy at the following velocities
(a) 10 ms-1 (b) 15 ms-1 (c) 20 ms-1 (d) 30 ms-1 (e) 35 ms-1 {NB 1 ms-1 = 2 m p h}
v (ms-1)
|
ke
| |
10
|
3.750 X 10 +04
|
J
|
15
|
8.438 X 10 +04
|
J
|
20
|
1.500 X 10 +05
|
J
|
30
|
3.375 X 10 +05
|
J
|
35
|
4.594 X 10 +05
|
J
|
2. (a) A car has a mass of 1000 kg. Calculate its KE at a velocity of 25 ms-1 .
3.125 x 105 J
(b) A train has a mass of 37 tonnes {1 tonne = 1000 kg}. If it also has a velocity of 25 ms-1 what is its kinetic energy ?
1.156 x 107 J
3. A woman has a mass of 65 kg.What is her GPE at the top of a 12 metre diving board ?
7651.8 J
to 3 sig figs 7650 J
4. A cat has a mass of 6 kg. What is its GPE at the top of a tree that is 4.2 m above the ground ? 247.212 J
5. The Eiffel Tower is 300 m high. What is the GPE of a 100 g bird perched on the top of it ?
( = 01Kg) 294.3 J
6. The Great Pyramid of Khufu (Cheops to the Greeks) is 146 m high. It is made of stones of mass 250 t. What is the GPE of the topmost stone ?
3.58 x 108J (m = 2.5 x 105 kg)
7. The Empire State Building is 449 m high(but this includes a 68 m TV mast).What is the GPE of a ball of mass 400 g at the top of the building (not the TV mast) ? If the ball is dropped over the side what will happen to the GPE ? What will be its speed at the instant before it hits the ground ? (Ignoring air resistance)
GPE = 1495 J
Ignoring air resistance GPE= KE mgh=1/2 mv2 m cancels v2 = 2gh
So v = √2gh = √2 x 9.81(449 -68) = 86.5 ms-1
8. Olympus Mons is a volcano on Mars. It is 25 km high. What would be the GPE of a human of mass 50 kg on its summit ? (surface gravity = 0.38 that of Earth) Compare this with the same human standing on the summit of Everest 8534 m high.
Olympus mons GPE = mgh = 50 (9.81 x 0.38) 25 000m = 4.66 x 106 J
Mt Everest = 4.19 x 106 J (Mars is much smaller than the Earth, a 30Km high mountain would collapse in the Earth’s gravitational field.
9. The space shuttle has a mass of 80 t. Escape velocity (the velocity an object has to travel at in order to escape the earth's gravitational field) is 11 km/s. What is its KE at this speed? If all this KE is turned into GPE how high would it be ? What assumption do you have to make in your calculation.
KE = 4.84 x 1012 J = GPE = mgh so h = KE/mg = 6.16 x 106 m
Assuming g is constant at 9.81. g decreases as a function of 1/r2. r = distance from the centre of the earth. When this is taken into account the height is ∞
How much energy would it take to accelerate the space shuttle to light speed (300 000 kms-1 ). {This is not possible, also the equation you will use to calculate KE is not valid near the speed of light but it will do for this purpose}
3.6 x1021 J
A nuclear power station produces around 500 MW
(500 000 000 J per second). How long would 100 power stations take to produce this amount of energy?
100 power stations 5 x 109 Js-1
Time to produce energy to accelerate space shuttle = 3.6 x1021 J / 5 x 109 Js-1 = 7.2 x 1011 s
22832 years (NB same amout of energy required to slow down when you get there)
How feasible is travelling close to the speed of light?
The nearest star is about 4 light years away. How long would it take the space shuttle to get there at 11 kms-1 (22 000 mph)? {1 light year is the distance light will travel in 1 year}
How feasible is interstellar travel?
Distance = 4 (3x108 ms-1) (365d x24 hr x 60 min x 60s) = 3.78432x 1016 m
Time = distance/ velocity = 3.78432x 1016 m / 11 000 ms-1 = 3.44029x1012 s = 109091 years
About 10 times longer than human civilisation!
