Browse Work, energy & power

1. 1
   Figure 1Diagram not accurately drawn.
   
   A straight plank is fixed with its lower end on horizontal ground and its upper end on top of a vertical wall. The plank is inclined to the horizontal at an angle $\theta$, where $\tan\theta = \frac{5}{12}$, and the upper surface of the plank is rough.
   
   A small block of mass $3$ kg is projected up the plank from the point $A$ with speed $U\ \text{m s}^{-1}$. The block slides along a line of greatest slope of the plank and comes to instantaneous rest at the point $B$, as shown in Figure 1. The point $B$ is $1.5$ m vertically above $A$.
   
   The coefficient of friction between the block and the plank is $\frac{1}{4}$
   
   The block is modelled as a particle.
   (a) Find the work done by the block against friction as it travels from $A$ to $B$.
   
   (3 marks)
   (b) Use the work–energy principle to find the value of $U$.
   
   (4 marks)
   
   The block then slides back down the plank.
   (c) Use the work–energy principle to find the speed with which the block passes back through $A$.
   
   (3 marks)
   Level 4 · 10 marksTry it→
2. 2
   A small ring $P$ of mass $m$ is threaded on a fixed rough straight wire. The wire lies in a vertical plane and is inclined to the horizontal at an angle $\alpha$, where $\tan\alpha = \frac{8}{15}$
   
   The coefficient of friction between $P$ and the wire is $\frac{1}{3}$
   
   The ring is modelled as a particle.
   (a) Show that, while $P$ is moving along the wire, the magnitude of the frictional force acting on $P$ is $\frac{5}{17}mg$
   
   (2 marks)
   
   The points $A$ and $B$ lie on the wire, with $B$ higher than $A$ and $AB = 17a$, where $a$ is a positive constant. The ring is projected up the wire from $A$ and first comes to instantaneous rest at $B$.
   (b) Use the work–energy principle to find, in terms of $a$ and $g$, the speed with which $P$ is projected from $A$.
   
   (4 marks)
   
   The ring then slides back down the wire towards $A$.
   (c) Use the work–energy principle to find, in terms of $a$ and $g$, the speed with which $P$ passes back through $A$.
   
   (4 marks)
   Level 4 · 10 marksTry it→
3. 3
   A block of mass $2\text{ kg}$ is released from rest and slides $5\text{ m}$ down the line of greatest slope of a rough plane inclined at angle $\theta$, where $\sin\theta = 0.6$. It reaches the bottom moving at $5\text{ m s}^{-1}$. Take $g = 10\text{ m s}^{-2}$.
   (a) Find the potential energy lost. (2 marks)
   (b) Find the kinetic energy gained. (1 mark)
   (c) Hence find the work done against friction. (2 marks)
   Level 4 · 5 marksTry it→

All 19 work done by a force questions →

1. 1
   A child of mass $30\text{ kg}$ starts from rest at the top of a smooth curved slide and descends a vertical height of $5\text{ m}$. Taking $g = 10\text{ m s}^{-2}$:
   (a) Find the child's speed at the bottom of the slide. (3 marks)
   (b) Find the child's kinetic energy at the bottom. (2 marks)
   Level 4 · 5 marksTry it→
2. 2
   A block of mass $3\text{ kg}$ is projected with speed $8\text{ m s}^{-1}$ along a rough horizontal surface. A constant frictional force brings it to rest after a distance of $4\text{ m}$.
   (a) Find the initial kinetic energy of the block. (2 marks)
   (b) State the work done against friction. (1 mark)
   (c) Hence find the magnitude of the frictional force. (2 marks)
   Level 4 · 5 marksTry it→
3. 3
   A stone is thrown from ground level with speed $15\text{ m s}^{-1}$, in any direction. Air resistance is negligible; take $g = 10\text{ m s}^{-2}$.
   
   Use energy conservation to find its speed when it is $10\text{ m}$ above the ground. (4 marks)
   Level 4 · 4 marksTry it→

All 15 kinetic and potential energy questions →

1. 1
   A car of mass $1500$ kg tows a caravan of mass $1000$ kg down a straight road. The road is inclined to the horizontal at an angle $\alpha$, where $\sin\alpha = \frac{1}{49}$
   
   The caravan is attached to the car by a tow bar which is parallel to the road. The tow bar is modelled as a light rod.
   
   The non-gravitational resistances to the motion are modelled as constant forces, of magnitude $500$ N on the car and $800$ N on the caravan.
   
   The engine of the car works at a constant rate of $18$ kW.
   (a) Find the acceleration of the car and the caravan when their speed is $10\ \text{m s}^{-1}$
   
   (5 marks)
   
   Later, when the car and the caravan are moving down the road at $12\ \text{m s}^{-1}$, the tow bar breaks. The caravan continues to move down the road and the resistance to its motion is unchanged.
   (b) Use the work–energy principle to find how far the caravan travels down the road after the tow bar breaks.
   
   (4 marks)
   Level 4 · 9 marksTry it→
2. 2
   A coach of mass $12\,000$ kg is moving up a straight hill which is inclined to the horizontal at an angle $\alpha$, where $\sin\alpha = \frac{1}{24}$
   
   The resistance to the motion of the coach from non-gravitational forces is modelled as a constant force of magnitude $R$ newtons. The coach is modelled as a particle.
   
   With its engine working at a constant rate of $72$ kW, the coach moves up the hill at a constant speed of $12\ \text{m s}^{-1}$
   (a) Find the value of $R$.
   
   (4 marks)
   
   While the coach is moving up the hill at $12\ \text{m s}^{-1}$, the rate at which its engine is working is suddenly increased to $96$ kW.
   (b) Find the acceleration of the coach immediately after the rate of working is increased.
   
   (4 marks)
   
   Later, the coach is moving up the hill with speed $15\ \text{m s}^{-1}$ when it passes the point $A$. At $A$ the engine is switched off. The coach continues to move up the hill and the resistance to its motion is still $R$ newtons.
   (c) Use the work–energy principle to find the speed of the coach at the instant when it has travelled $50$ m up the hill from $A$.
   
   (4 marks)
   Level 4 · 12 marksTry it→
3. 3
   A car of mass $1200\text{ kg}$ travels at a constant speed of $20\text{ m s}^{-1}$ up a hill inclined at angle $\theta$ to the horizontal, where $\sin\theta = 0.05$. The resistance to motion is constant at $400\text{ N}$. Taking $g = 10\text{ m s}^{-2}$, find the power developed by the engine. (5 marks)
   
   (The diagram is not drawn to scale.)
   Level 4 · 5 marksTry it→

All 22 power questions →