A-Level CAIE Mathematics A2 4.5 Energy, work and power Question Bank

A crane is used to raise a block of mass 600 kg vertically upwards at a constant speed through a height of 15 m . There is a resistance to the motion of the block, which the crane does 10000 J of work to overcome.

A metal post is driven vertically into the ground by dropping a heavy object onto it from above. The mass of the object is 120 kg and the mass of the post is 40 kg (see diagram). The object hits the post with speed $8 \mathrm{~m} \mathrm{~s}^{-1}$ and remains in contact with it after the impact.

A particle of mass 0.6 kg is projected with a speed of $4 \mathrm{~m} \mathrm{~s}^{-1}$ down a line of greatest slope of a smooth plane inclined at $10^{\circ}$ to the horizontal.

Use an energy method to find the speed of the particle after it has moved 15 m down the plane.

A crane is lifting a load of 1250 kg vertically at a constant speed $V \mathrm{~m} \mathrm{~s}^{-1}$. Given that the power of the crane is a constant 20 kW , find the value of V.

A man has mass 80 kg . He runs along a horizontal road against a constant resistance force of magnitude $P \mathrm{~N}$. The total work done by the man in increasing his speed from $4 \mathrm{~m} \mathrm{~s}^{-1}$ to $5.5 \mathrm{~m} \mathrm{~s}^{-1}$ while running a distance of 60 metres is 1200 J . Find the value of P.

A man pushes a wheelbarrow of mass 25 kg along a horizontal road with a constant force of magnitude 35 N at an angle of $20^{\circ}$ below the horizontal. There is a constant resistance to motion of 15 N . The wheelbarrow moves a distance of 12 m from rest.

One end of a light inextensible string is attached to a block. The string makes an angle of $\theta^{\circ}$ with the horizontal. The tension in the string is 20 N . The string pulls the block along a horizontal surface at a constant speed of $1.5 \mathrm{~m} \mathrm{~s}^{-1}$ for 12 s . The work done by the tension in the string is 50 J . Find $\theta$.

A particle of mass 0.6 kg is dropped from a height of 8 m above the ground. The speed of the particle at the instant before hitting the ground is $10 \mathrm{~m} \mathrm{~s}^{-1}$. Find the work done against air resistance.

A weightlifter performs an exercise in which he raises a mass of 200 kg from rest vertically through a distance of 0.7 m and holds it at that height.

A particle of mass 0.4 kg is projected with a speed of $12 \mathrm{~m} \mathrm{~s}^{-1}$ up a line of greatest slope of a smooth plane inclined at $30^{\circ}$ to the horizontal.