Jan Dangerfield, Stuart Haring and, Julian Gilbey Solutions for Exercise 6: END-OF-CHAPTER REVIEW EXERCISE 2

A cyclist travelling on a horizontal road produces a constant horizontal force of $40 \mathrm{N}.$ The total mass of the cyclist and the bicycle is $80 \mathrm{kg}.$ Considering other forces to be negligible, find the distance covered as the cyclist increases her speed from $10 \mathrm{m}{\mathrm{s}}^{-1}$ to $12 \mathrm{m}{\mathrm{s}}^{-1}$.

A bag of sand of mass $20 \mathrm{kg}$ is lifted on a pallet by a crane. The bag is lifted from rest to a height of $5 \mathrm{m}$ in $8 \mathrm{s}$ at constant acceleration. Find the normal contact force on the bag of sand.

A rower starts from rest and accelerates to $4 \mathrm{m}{\mathrm{s}}^{-1}$ in $20 \mathrm{s}$. The combined mass of the rower and the boat is $100 \mathrm{kg}.$ The rower provides a constant horizontal driving force of $60 \mathrm{N}$ but is held back by a constant resistance from the water. Find the size of the resistance force.

A car of mass $400 \mathrm{kg}$ is approaching a junction and needs to stop in $40 \mathrm{m}.$ It is travelling at $15 \mathrm{m}{\mathrm{s}}^{-1}$ and there is air resistance of $1200 \mathrm{N}$.

Determine whether the car needs to brake or accelerate and find the size of the relevant force.

A car of mass $350 \mathrm{kg}$ is travelling at $30 \mathrm{m}{\mathrm{s}}^{-1}$ when it starts to slow down, $100 \mathrm{m}$ from a junction. At first, it slows just using the air resistance of $200 \mathrm{N}$. Then, at a distance of $s \mathrm{m}$ from the junction, it slows using brakes, providing a force of $2000 \mathrm{N}$ as well as the air resistance. Find the distance from the junction at which the brakes must be applied if the car is to stop at the junction.

A boy drags a cart of mass $5 \mathrm{kg}$ with force $10 \mathrm{N}$ along a horizontal road. There is air resistance of $2 \mathrm{N},$ At some point the boy lets go of the cart and the cart slows down due to air resistance until coming to rest. In total, the cart has travelled $36 \mathrm{m}.$. Find the length of time the boy was dragging the cart.

A light pallet is at rest on the ground with a stone of mass $30 \mathrm{kg}$ on top of it but not attached. A crane lifts the pallet by providing a force of $310 \mathrm{N}$ upwards to a height of $8 \mathrm{m},$ at which point the pallet instantly stops and the stone loses contact with it. Find the maximum height reached by the stone.