Kinetic Energy Calculations

Question 1

A swimmer of mass 70 kg is moving at a speed of 1.4 m/s.

Calculate the kinetic energy of the swimmer in J (to 2 sf).

Answer 1

KE = 1/2 mv^2
KE = 0.5 x 70 x 1.4^2
KE = 68.6 = 69 J (2 sf)

Question 2

A bullet with a mass of 10.0 g is travelling with an initial speed of 400 m/s.

What is the bullet’s Initial kinetic energy store?

Answer 2

m = 10 g ≡ 10/1000 = 0.01 kg

KE = 1/2 mv^2
KE = 0.5 x 0.01 x 400^2
KE = 800 J of kinetic energy

Question 3

A car of mass 1200 kg is travelling at a steady speed of 30.0 m/s (~67 mph, 108 km/hour).

What is the kinetic energy store of the car?

Answer 3

m = 10 g ≡ 10/1000 = 0.01 kg

KE = 1/2 mv^2
KE = 0.5 x 1200 x 30^2
KE = 540,000 J

Question 4

A car of mass 1200 kg has a kinetic energy of 220,000J.
What speed is the car doing?

Answer 4

KE = 1/2 mv^2
rearranging

v^2 = 2KE / m
v = √(2Eke / m)
v = √(2 x 270,000 / 1200)
v = 21.2 m/s (3 s.f.)

Question 5

The chemical potential energy store of a 100 g rocket, on firing, gives it an initial kinetic energy store of 200 J.

Calculate the initial vertical velocity of the rocket.

Answer 5

m = 100 g ≡ 100 / 1000 = 0.1 kg

KE = 1/2 mv^2
v^2 = 2KE / m
v = √(2KE / m)
v = √(2 x 200 / 0.10)
v = 63.2 m/s (3 s.f.)

Question 6

A projectile is required to impart a kinetic energy blow of 5000 J at a speed of 500 m/s.

What mass of projectile is required?

Answer 6

KE = 1/2 mv^2
m = 2 x Eke / v^2
m = 2 x 5000 / 5002
m = 0.040 kg (40.0 g, 3 s.f.)

Question 7

A pole vaulter has a weight of 800 N and vaults to a height of 4.5 m.

How much work does the pole vaulter do?

Answer 7

work (J) = force (N) x distance of action (m)

work done = 800 x 4.5 = 3600 J

Question 8

A pole vaulter has a weight of 800 N and vaults to a height of 4.5 m

What was the initial speed of take-off by the pole vaulter? (take gravity strength as 9.8 N/kg).

Answer 8

mass = 800 / 9.8 = 81.63 kg

KE = 1/2 mv^2
v = √(2KE/m)
v = √(2 x 3600/81.63)
v = 9.4 m/s (2sf)