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

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 cyclist has mass 85 kg and rides a bicycle of mass 20 kg . The cyclist rides along a horizontal road against a total resistance force of 40 N . Find the total work done by the cyclist in increasing his speed from $5 \mathrm{~m} \mathrm{~s}^{-1}$ to $10 \mathrm{~m} \mathrm{~s}^{-1}$ while travelling a distance of 50 m .

A car of mass 800 kg is moving on a straight horizontal road with its engine working at a rate of 22.5 kW . Find the resistance to the car's motion at an instant when the car's speed is $18 \mathrm{~m} \mathrm{~s}^{-1}$ and its acceleration is $1.2 \mathrm{~m} \mathrm{~s}^{-2}$.

A car of mass 600 kg travels along a straight horizontal road. The resistance to the car's motion is constant and equal to $R \mathrm{~N}$.

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 train is moving at constant speed $V \mathrm{~m} \mathrm{~s}^{-1}$ along a horizontal straight track. Given that the power of the train's engine is 1330 kW and the total resistance to the train's motion is 28 kN , find the value of V.

One end of a light inextensible string is attached to a block. The string makes an angle of $60^{\circ}$ above the horizontal and is used to pull the block in a straight line on a horizontal floor with acceleration $0.5 \mathrm{~m} \mathrm{~s}^{-2}$. The tension in the string is 8 N . The block starts to move with speed $0.3 \mathrm{~m} \mathrm{~s}^{-1}$. For the first 5 s of the block's motion, find

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 block is pulled in a straight line along horizontal ground by a force of constant magnitude acting at an angle of $60^{\circ}$ above the horizontal. The work done by the force in moving the block a distance of 5 m is 75 J . Find the magnitude of the force.

A ring is threaded on a fixed horizontal bar. The ring is attached to one end of a light inextensible string which is used to pull the ring along the bar at a constant speed of $0.5 \mathrm{~m} \mathrm{~s}^{-1}$. The string makes a constant angle of $24^{\circ}$ with the bar and the tension in the string is 6 N (see diagram). Find the work done by the tension in a period of 8 s .