Work, Energy and Power — Practice

Question 1

A force F = (2i + 3j) N displaces a particle by d = (4i - j) m. Find the work done.

Accepted Answer

W = F.d = (2)(4) + (3)(-1) = 8 - 3 = 5 J.

Question 2

A spring (k = 200 N/m) is compressed by 5 cm. Find the energy stored.

Accepted Answer

U = (1/2)kx^2 = (1/2)(200)(0.05)^2 = 0.25 J.

Question 3

A 1000 kg car accelerates from rest to 20 m/s in 10 s. Find the average power.

Accepted Answer

Work = delta-K = (1/2)(1000)(20^2) = 200000 J. P = W/t = 200000/10 = 20000 W = 20 kW.

Question 4

In an elastic collision a 2 kg ball at 4 m/s hits a 4 kg ball at rest. Find the final velocities.

Accepted Answer

v1' = [(m1 - m2)/(m1 + m2)]u1 = (-2/6)(4) = -4/3 m/s. v2' = [2m1/(m1 + m2)]u1 = (4/6)(4) = 8/3 m/s.

Question 5

Can kinetic energy be negative? Can potential energy be negative?

Accepted Answer

Kinetic energy K = (1/2)mv^2 is always >= 0. Potential energy is reference-dependent and can be negative, e.g. gravitational PE below the chosen reference level.

Practice — Work, Energy and Power

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