A football is kicked from ground level with speed $15{ \mathrm{ms}}^{-1}$ and rises to a height of $1.45 \mathrm{m}$. Assume that air resistance is negligible.

Explain why the horizontal component of the velocity is constant throughout the motion.

A football is kicked from ground level with speed $15{ \mathrm{ms}}^{-1}$ and rises to a height of $1.45 \mathrm{m}$. Assume that air resistance is negligible.

Show that the ball was kicked at an angle of $21.0°$ with the horizontal.

A crate of mass $M \mathrm{kg}$ sits at the bottom of a smooth slope that is inclined at an angle $\theta$ to the horizontal. A light inextensible rope is attached to the crate and passes over a smooth pulley at the top of the slope. The part of the rope between the crate and the pulley is parallel to the slope. The other end of the rope hangs vertically and at the other end there is a ball of mass $m \mathrm{kg}$. The system is released from rest and the ball reaches the ground with speed $v{ \mathrm{ms}}^{-1}$ after descending a distance of $h \mathrm{m}$.

Find expressions for the decrease in potential energy for the ball.

A crate of mass $M \mathrm{kg}$ sits at the bottom of a smooth slope that is inclined at an angle $\theta$ to the horizontal. A light inextensible rope is attached to the crate and passes over a smooth pulley at the top of the slope. The part of the rope between the crate and the pulley is parallel to the slope. The other end of the rope hangs vertically and at the other end there is a ball of mass $m \mathrm{kg}$. The system is released from rest and the ball reaches the ground with speed $v{ \mathrm{ms}}^{-1}$ after descending a distance of $h \mathrm{m}$.

Find expressions for the increase in kinetic energy for the ball.

A crate of mass $M \mathrm{kg}$ sits at the bottom of a smooth slope that is inclined at an angle $\theta$ to the horizontal. A light inextensible rope is attached to the crate and passes over a smooth pulley at the top of the slope. The part of the rope between the crate and the pulley is parallel to the slope. The other end of the rope hangs vertically and at the other end there is a ball of mass $m \mathrm{kg}$. The system is released from rest and the ball reaches the ground with speed $v{ \mathrm{ms}}^{-1}$ after descending a distance of $h \mathrm{m}$. Find expressions for the increase in mechanical energy for the crate. (Use: $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A crate of mass $M \mathrm{kg}$ sits at the bottom of a smooth slope that is inclined at an angle $\theta$ to the horizontal. A light inextensible rope is attached to the crate and passes over a smooth pulley at the top of the slope. The part of the rope between the crate and the pulley is parallel to the slope. The other end of the rope hangs vertically and at the other end there is a ball of mass $m \mathrm{kg}$. The system is released from rest and the ball reaches the ground with speed $v{ \mathrm{ms}}^{-1}$ after descending a distance of $h \mathrm{m}$.

Use the work-energy principle to show that $v=\sqrt{20h\left(\frac{m-M\sin \theta }{m+M}\right)}$. (Use: $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A piece of sculpture includes a vertical metal circle with radius $2.45 \mathrm{m}$. A particle of mass $0.2 \mathrm{kg}$ sits at point $A$ on top of the sculpture at the top of the circle (on the outside of the circle). The particle is gently displaced and slides down the circle until it reaches point $B$, which is level with the centre of the circle. It then falls a further $3.6 \mathrm{m}$ vertically to hit the ground at point $C$.

Use the work-energy principle to find:

the speed of the particle when it reaches point $B$

A piece of sculpture includes a vertical metal circle with radius $2.45 \mathrm{m}$. A particle of mass $0.2 \mathrm{kg}$ sits at point $A$ on top of the sculpture at the top of the circle (on the outside of the circle). The particle is gently displaced and slides down the circle until it reaches point $B$, which is level with the centre of the circle. It then falls a further $3.6 \mathrm{m}$ vertically to hit the ground at point $C$.

Use the work-energy principle to find:

the speed of the particle when it reaches point $C$.

A piece of sculpture includes a vertical metal circle with radius $2.45 \mathrm{m}$. A particle of mass $0.2 \mathrm{kg}$ sits at point $A$ on top of the sculpture at the top of the circle (on the outside of the circle). The particle is gently displaced and slides down the circle until it reaches point $B$, which is level with the centre of the circle. It then falls a further $3.6 \mathrm{m}$ vertically to hit the ground at point $C$.

What modelling assumptions have you made?