The recommended slope for wheelchair ramps is $1:12$ This means that the ramp rises $1 \mathrm{cm}$ vertically for every $12 \mathrm{cm}$ along the slope.

A person in their wheelchair, with total mass $90 \mathrm{kg}$, descend along a $1:12$ wheelchair ramp that has slope length $8 \mathrm{m}$.

They start the descent with speed $2 \mathrm{m}{ \mathrm{s}}^{-1}$ and finish with speed $4{ \mathrm{ms}}^{-1}$.

Work out the change in total mechanical energy (kinetic energy + potential energy) after descending the ramp.

A ball of mass $0.02 \mathrm{kg}$ is projected vertically upwards through oil. The ball has initial speed $\frac{35}{12} \mathrm{m}{ \mathrm{s}}^{-1}$. The oil exerts a resistance of $0.1t^{0.5} \mathrm{N}$, where $t \mathrm{s}$ is the time from when the ball was projected.

Work out the increase in the potential energy of the ball from the start to when it comes to instantaneous rest. (Note: you will need an equation solver for this question. You will not be allowed an equation solver in the examination.)

A ball of mass $30 \mathrm{g}$ is thrown vertically upwards with an initial speed of $4{ \mathrm{ms}}^{-1}$. Air resistance can be ignored. The ball reaches a maximum height of $80 \mathrm{cm}$. Find the decrease in kinetic energy.

A ball of mass $30 \mathrm{g}$ is thrown vertically upwards with an initial speed of $4{ \mathrm{ms}}^{-1}$. Air resistance can be ignored. The ball reaches a maximum height of $80 \mathrm{cm}$. Find:

the increase in potential energy.

A car of mass $1600 \mathrm{kg}$ is driven $200 \mathrm{m}$ along a straight horizontal road. The car starts with a speed of $3 \mathrm{m}{ \mathrm{s}}^{-1}$ and finishes with a speed of $20 \mathrm{m}{ \mathrm{s}}^{-1}$. A constant resistance of $40 \mathrm{N}$ acts.

Find the acceleration of the car.

A car of mass $1600 \mathrm{kg}$ is driven $200 \mathrm{m}$ along a straight horizontal road. The car starts with a speed of $3 \mathrm{m}{ \mathrm{s}}^{-1}$ and finishes with a speed of $20 \mathrm{m}{ \mathrm{s}}^{-1}$. A constant resistance of $40 \mathrm{N}$ acts.

Find the work done by the driving force.

A box of mass $20 \mathrm{kg}$ is pushed $3 \mathrm{m}$ up a slope inclined at an angle $\alpha$ to the horizontal. The work done by the push force is $900 \mathrm{J}$ and non-gravitational resistance (friction and air resistance) is $40 \mathrm{N}$.

Work out the push force.