Question

Kinetic Energy
𝐾𝑬 = 𝒎𝒗𝟐
𝟐
KE = kinetic energy (J)
m = mass (kg)
v = velocity (m/s)
1. A car of mass 900 kg travels at 22 m/s . Calculate the kinetic energy of the car.
2. Suppose an object of mass 20 kg has 3610 J of kinetic energy, what is its velocity?
Gravitational Potential Energy
𝑃𝐸 = 9.8 ∙ 𝑚 ∙ ℎ
PE = potential energy (J)
m = mass (kg)
h = height (m)
3. A bird has mass 3 kg flies to the top of a tree 15 m tall. How much gravitational potential energy
does the bird have at the top of the tree?
4. If an object of mass 23 kg has 4000 J of gravitational potential energy, how high above the
ground is it?

Answer 1

Using KE = 1/2 m v^2 and PE = g m h (g = 9.8 m/s^2):

1) KE for car:
KE = 1/2 · 900 kg · (22 m/s)^2 = 0.5·900·484 = 217,800 J ≈ 2.18 × 10^5 J

2) Velocity from KE = 3610 J, m = 20 kg:
v = sqrt(2·KE / m) = sqrt(2·3610 / 20) = sqrt(7220 / 20) = sqrt(361) = 19 m/s

3) PE for bird (m = 3 kg, h = 15 m):
PE = 9.8 · 3 · 15 = 441 J

4) Height from PE = 4000 J, m = 23 kg:
h = PE / (9.8 · m) = 4000 / (9.8·23) = 4000 / 225.4 ≈ 17.8 m