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.

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 $40 \mathrm{N}$.

Show that the acceleration of the box up the slope, $a \mathrm{m}{ \mathrm{s}}^{-2}$, is given by $a=13-10\sin \alpha$.

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 $40 \mathrm{N}$.

What assumptions have you made?

$A$ and $B$ are two points $50$ metres apart on a straight path inclined at an angle $\theta$ to the horizontal, where $\sin \theta =0.05$, with $A$ above the level of $B$. A block of mass $16 \mathrm{kg}$ is  pulled down the path from $A$ to $B$. The block starts from rest at $A$ and reaches $B$ with a  speed of $10 \mathrm{m}{ \mathrm{s}}^{-1}$. The work done by the pulling force acting on the block is $1150 \mathrm{J}$.

Find the work done against the resistance to motion.

The block is now pulled up the path from $B$ to $A$. The work done by the pulling force and the work done against the resistance to motion are the same as in the case of the downward motion.

$A$ and $B$ are two points $50$ metres apart on a straight path inclined at an angle $\theta$ to the horizontal, where $\sin \theta =0.05$, with $A$ above the level of $B$. A block of mass $16 \mathrm{kg}$ is  pulled down the path from $A$ to $B$. The block starts from rest at $A$ and reaches $B$ with a  speed of $10 \mathrm{m}{ \mathrm{s}}^{-1}$. The work done by the pulling force acting on the block is $1150 \mathrm{J}$.

Show that the speed of the block when it reaches $A$ is the same as its speed when it started at $B$.