1
KE = mv 2
2
GPE = mgh
1. A bow can shoot a 0.042 kg arrow at a speed of 16.5m/s. What is the kinetic
energy of the arrow?
2. A high jumper has a mass of 62 kg. She jumps to a maximum height of 2.3 m.
If the acceleration due to gravity is 10 m/s2, calculate the gravitational potential
energy of the jumper.
3. A cheetah can run with a speed of 34 m/s and has a kinetic energy of 32946 J.
What is the mass of the cheetah?
4. In an elevator, it takes 33 kJ of energy to lift a group of people up 6 m. What is
the total mass of the group of people?
5. A climber has a potential energy of 11000 J. If the mass of the climber is 85 kg
determine their height above the ground.
6. On a particular planet, it takes 850 J for a 50 kg remote probe to launch itself
up 2 m. What is the gravitational field strength on the planet?
7. It takes 338000 J of energy to move a car of mass 1000 kg at a speed of v.
Calculate v.
8. A stone is dropped down a well. When it hits the bottom of the well it is
travelling at 20 m/s. The mass of the stone is 0.02 kg.
a. Calculate the kinetic energy of the stone as it hits the bottom of the well.
b. What is the gravitational potential energy of the stone at the top of the
well?
c. Calculate the height of the well.
9. There are two remote control toys – a car and a truck. The truck is twice as
heavy as the car, but the car is travelling at twice the speed of the truck.
Assume the batteries in each have the same power. Which battery will go flat
first? Why?
1
KE = mv 2
2
GPE = mgh
1. A bow can shoot a 0.042 kg arrow at a speed of 16.5m/s. What is the kinetic
energy of the arrow?
2. A high jumper has a mass of 62 kg. She jumps to a maximum height of 2.3 m.
If the acceleration due to gravity is 10 m/s2, calculate the gravitational potential
energy of the jumper.
3. A cheetah can run with a speed of 34 m/s and has a kinetic energy of 32946 J.
What is the mass of the cheetah?
4. In an elevator, it takes 33 kJ of energy to lift a group of people up 6 m. What is
the total mass of the group of people?
5. A climber has a potential energy of 11000 J. If the mass of the climber is 85 kg
determine their height above the ground.
6. On a particular planet, it takes 850 J for a 50 kg remote probe to launch itself
up 2 m. What is the gravitational field strength on the planet?
7. It takes 338000 J of energy to move a car of mass 1000 kg at a speed of v.
Calculate v.
8. A stone is dropped down a well. When it hits the bottom of the well it is
travelling at 20 m/s. The mass of the stone is 0.02 kg.
a. Calculate the kinetic energy of the stone as it hits the bottom of the well.
b. What is the gravitational potential energy of the stone at the top of the
well?
c. Calculate the height of the well.
9. There are two remote control toys – a car and a truck. The truck is twice as
heavy as the car, but the car is travelling at twice the speed of the truck.
Assume the batteries in each have the same power. Which battery will go flat
first? Why?
Answers
1
1. 𝐾𝐸 = 𝑚𝑣 2 = 0.5 × 0.042 × 16.52 = 5.7 J
2
2. 𝐺𝑃𝐸 = 𝑚𝑔ℎ = 62 × 10 × 2.3 = 1426 J
1
2𝐾𝐸
32946
3. 𝐾𝐸 = 𝑚𝑣 2 ⇒ 𝑚 = 2 =
= 57 kg
2
2
4. 𝐺𝑃𝐸 = 𝑚𝑔ℎ ⇒ 𝑚 =
5. 𝐺𝑃𝐸 = 𝑚𝑔ℎ ⇒ ℎ =
6. 𝐺𝑃𝐸 = 𝑚𝑔ℎ ⇒ 𝑔 =
1
𝑣
𝐺𝑃𝐸
𝑔ℎ
𝐺𝑃𝐸
𝑚𝑔
𝐺𝑃𝐸
𝑚ℎ
𝐾𝐸
=
=
=
0.5×34
33000
10×6
11000
10×85
850
= 550 kg
= 12.9 m
= 8.5 N/kg
50×2
338000
7. 𝐾𝐸 = 𝑚𝑣 2 ⇒ 𝑣 = √1 = √
= 18.3 m/s
2
0.5×1000
𝑚
2
8. This question relies on the conservation of energy. Because the stone is
dropped from a height the total amount of GPE to begin with is turned into KE
at the end.
1
a. gf 𝐾𝐸 = 𝑚𝑣 2 = 0.5 × 0.02 × 202 = 4 J
2
b. By energy conservation, GPE at the top is 4 J as well.
𝐺𝑃𝐸
4
4
c. 𝐺𝑃𝐸 = 𝑚𝑔ℎ ⇒ ℎ =
=
=
= 20 m
𝑚𝑔
0.02×10
0.2
9. This is a hard question mainly because there aren’t any numbers only ratios. It
can be simplified if the students choose a number of the mass and speed say
1.
So the car has a mass of 1 kg and the truck has twice this (2 kg)
The truck has a speed of 1 m/s, and the car has three times this (3 m/s)
So the kinetic energy of the car is
And the kinetic energy of the truck is
0.5 × 1 × 32 = 4.5 J
0.5 × 2 × 12 = 1 J
So the car has more kinetic energy therefore,
More energy needs to be transferred from the battery,
Therefore the battery in the car will run out first (both batteries have the
same power from the question).
(In fact the battery will be used up 4.5 times more quickly in the car!)