Browse Work, energy & power

1. 1
   A small boat of mass $150$ kg is pulled up a straight slipway by a winch. The slipway is inclined to the horizontal at an angle $\alpha$, where $\tan\alpha = \frac{9}{40}$
   
   The winch cable is attached to the boat and is parallel to a line of greatest slope of the slipway. The winch pulls the boat along this line, at a constant speed, until the boat has moved $8.2$ m up the slipway.
   
   The coefficient of friction between the boat and the slipway is $\frac{1}{4}$
   
   The boat is modelled as a particle and the cable is modelled as being light.
   
   Use the model to find the total work done by the winch in pulling the boat the $8.2$ m up the slipway.
   
   (5 marks)
   Level 3 · 5 marksTry it→
2. 2
   A block is pushed a distance of $6\text{ m}$ along a rough horizontal floor by a constant horizontal force of $25\text{ N}$. A constant frictional force of $10\text{ N}$ opposes the motion.
   (a) Find the work done by the applied force. (1 mark)
   (b) Find the work done against friction. (1 mark)
   (c) Find the net work done on the block. (2 marks)
   Level 3 · 4 marksTry it→
3. 3
   A sledge is pulled a distance of $15\text{ m}$ along horizontal ground by a rope inclined at angle $\theta$ to the horizontal, where $\cos\theta = 0.6$. The tension in the rope is $40\text{ N}$.
   (a) Find the work done by the tension. (2 marks)
   (b) The motion is opposed by a constant resistance of $12\text{ N}$. Find the net work done on the sledge. (2 marks)
   Level 3 · 4 marksTry it→

All 19 work done by a force questions →

1. 1
   A particle of mass $2\text{ kg}$ starts from rest on a smooth horizontal surface. A constant horizontal force of $6\text{ N}$ acts on it over a distance of $6\text{ m}$. Using the work–energy principle, find the speed of the particle after it has moved $6\text{ m}$. (4 marks)
   Level 3 · 4 marksTry it→
2. 2
   A stone of mass $0.2\text{ kg}$ is released from rest and falls freely (no air resistance) through a vertical distance of $5\text{ m}$. Taking $g = 10\text{ m s}^{-2}$, use conservation of energy to find its speed just before it lands. (4 marks)
   Level 3 · 4 marksTry it→
3. 3
   A particle of mass $3\text{ kg}$ accelerates from $4\text{ m s}^{-1}$ to $9\text{ m s}^{-1}$.
   
   Find the increase in its kinetic energy. (3 marks)
   Level 3 · 3 marksTry it→

All 15 kinetic and potential energy questions →

1. 1
   A motorcycle and its rider have a combined mass of $250$ kg and are modelled as a particle.
   
   The motorcycle is being ridden down a straight road. The road slopes downwards at an angle $\alpha$ to the horizontal, where $\sin\alpha = \frac{1}{25}$
   
   The engine of the motorcycle works at a constant rate of $6$ kW, and the non-gravitational resistance to the motion of the motorcycle is modelled as a constant force of magnitude $420$ N.
   
   Find the acceleration of the motorcycle at the instant when its speed is $12\ \text{m s}^{-1}$
   
   (5 marks)
   Level 3 · 5 marksTry it→
2. 2
   A car of mass $1000\text{ kg}$ moves at a constant speed of $30\text{ m s}^{-1}$ along a level road against a constant resistance of $600\text{ N}$. Find the power developed by the engine. (3 marks)
   Level 3 · 3 marksTry it→
3. 3
   A van's engine works at a constant $24\text{ kW}$ against a constant total resistance of $800\text{ N}$ on a level road.
   
   Find the van's maximum speed. (3 marks)
   Level 3 · 3 marksTry it→

All 22 power questions →