Jan Dangerfield, Stuart Haring and, Julian Gilbey Solutions for Exercise 1: CROSS-TOPIC REVIEW EXERCISE 3

A box of mass $25 \mathrm{kg}$ is pulled, at a constant speed, a distance of $36 \mathrm{m}$ up a rough plane inclined at an angle of $20°$ to the horizontal. The box moves up a line of greatest slope against a constant frictional force of $40 \mathrm{N}$. The force pulling the box is parallel to the line of greatest slope.

Find the change in gravitational potential energy of the box.

A box of mass $25 \mathrm{kg}$ is pulled, at a constant speed, a distance of $36 \mathrm{m}$ up a rough plane inclined at an angle of $20°$ to the horizontal. The box moves up a line of greatest slope against a constant frictional force of $40 \mathrm{N}$. The force pulling the box is parallel to the line of greatest slope.

Find the work done by the pulling force.

A car of mass $1000 \mathrm{kg}$ is moving along a straight horizontal road against resistances of total magnitude $300 \mathrm{N}$.

Find, in $\mathrm{kW}$, the rate at which the engine of the car is working when the car has a constant speed of $40 \mathrm{m}{ \mathrm{s}}^{-1}$.

A car of mass $1000 \mathrm{kg}$ is moving along a straight horizontal road against resistances of total magnitude $300 \mathrm{N}$.

(i) Find, in $\mathrm{kW}$, the rate at which the engine of the car is working when the car has a constant speed of $40 \mathrm{m}{ \mathrm{s}}^{-1}$.

(ii) Find the acceleration of the car when its speed is $25 \mathrm{m}{ \mathrm{s}}^{-1}$ and the engine is working at $90\%$ of the power found in part i.

A block of mass $25 \mathrm{kg}$ is pulled along horizontal ground by a force of magnitude $50 \mathrm{N}$ inclined at $10°$ above the horizontal. The block starts from rest and travels a distance of $20 \mathrm{m}$. There is a constant resistance force of magnitude $30 \mathrm{N}$ opposing motion.

Find the work done by the pulling force.

A block of mass $25 \mathrm{kg}$ is pulled along horizontal ground by a force of magnitude $50 \mathrm{N}$ inclined at $10°$ above the horizontal. The block starts from rest and travels a distance of $20 \mathrm{m}$. There is a constant resistance force of magnitude $30 \mathrm{N}$ opposing motion.

Use an energy method to find the speed of the block when it has moved a distance of $20 \mathrm{m}$.

A block of mass $25 \mathrm{kg}$ is pulled along horizontal ground by a force of magnitude $50 \mathrm{N}$ inclined at $10°$ above the horizontal. The block starts from rest and travels a distance of $20 \mathrm{m}$. There is a constant resistance force of magnitude $30 \mathrm{N}$ opposing motion.

Find the greatest power exerted by the $50 \mathrm{N}$ force.

A block of mass $25 \mathrm{kg}$ is pulled along horizontal ground by a force of magnitude $50 \mathrm{N}$ inclined at $10°$ above the horizontal. The block starts from rest and travels a distance of $20 \mathrm{m}$. There is a constant resistance force of magnitude $30 \mathrm{N}$ opposing motion.

After the block has travelled the $20 \mathrm{m}$, it comes to a plane inclined at $5°$ to the horizontal. The force of $50 \mathrm{N}$ is now inclined at an angle of $10°$ to the plane and pulls the block directly up the plane (see diagram). The resistance force remains $30 \mathrm{N}$.

Find the time it takes for the block to come to rest from the instant when it reaches the foot of the inclined plane.