1991 Q33 A sphere of mass 3 kg on the end of a wire is released from rest and swings through a vertical distance of 0.4 m. (Neglect air friction.) (a) Calculate the speed of the sphere as it passes through the lowest point of its path. (b) Explain the effect on the speed at the lowest point, if a sphere of mass 6 kg is used. 1995 Q32 A trolley of mass 2.0 kg rolls down a slope which makes an angle of 30º with the horizontal. The constant frictional force opposing the motion is 4.0 N. Calculate the size of the resultant force, in newtons, acting on the trolley.
1996 Q32 A mooring buoy is tethered to the seabed by a rope which is too short. The buoy floats under the water at high tide. The weight of the buoy is 50 N. (a) (i) Draw a labelled diagram to show all the forces acting on the buoy in the vertical direction. (ii) The tension in the rope is 1200 N. Calculate the buoyancy force. (b) The rope now snaps and the buoy starts to rise. What is the size of the buoyancy force on the buoy when it is just below the surface of the water?
1997 Q31 Two ropes are used to pull a boat at constant speed along a canal. Each rope exerts a force of 150 N at 20º to the direction of travel of the boat as shown. (a) Calculate the magnitude of the resultant force exerted by the ropes. (b) What is the magnitude of the frictional force acting on the boat? 1997 Q32 The diagram shows a weather balloon of mass m tethered by a rope to the ground. (a) Draw a sketch of the balloon. Mark and name all the forces acting vertically on the balloon. (b) What is the resultant force acting on the balloon?
2001 Q31 A tractor pulls a wagon along a level railway track. The tractor applies a horizontal force of 4.0 kn to the wagon at an angle of 18º as shown. (a) Calculate the component of this force parallel to the track. (b) The wagon, of mass 1.2 x 10 4 kg, accelerates at 0.15 in ms -2. Calculate the size of the frictional force acting on the wagon.
1991 Q1 An oil-rig has to be towed to a new operating area in the North Sea. It is towed by horizontal cables attached to two, tugs as shown below. The oil-rig has a mass of 20 x 10 6 kg and is initially at rest. (a) (i) If the forces applied to the oil-rig by the cables are each 1.0 x 10 6 N in the directions shown, what is their resultant force on the oil-rig? (ii) What is the magnitude of the acceleration of the oil-rig just as it moves from rest? (b) The cables continue to exert the same forces on the oil-rig. The acceleration of the oil-rig is continuously monitored and it is found that the acceleration decreases from its initial value. Explain this observation.
1993 Q2 A lunar landing craft descends vertically towards the surface of the Moon with a constant speed of 2.0 ms -1. The craft and crew have a total mass of 15 000 kg. Assume that the gravitational field strength on the Moon is 1.6 Nkg -1. (a) During the first part of the descent the upward thrust of the rocket engine is 24 000 N. Show that this results in the craft moving with a constant speed. (b) The upward thrust of the engine is increased to 25 500 N for the last 18 seconds of the descent. (i) Calculate the deceleration of the craft during this time. (ii) What is the speed of the craft just before it lands? (iii) How far is the craft above the surface of the Moon when the engine thrust is increased to 25 500 N?
1995 Q4 A crane is used to lower a concrete block of mass 5.0 x 10 3 kg into the sea. (a) The crane lowers the block towards the sea at a constant speed. Calculate the tension in the cable supporting the block. (b) The crane lowers the block into the sea. The block is held stationary just below the surface of the sea as shown in the diagram below. The tension in the cable is now 2.9 x 10 4 N. (i) Calculate the size of the buoyancy force acting on the block. (ii) Explain how this buoyancy force is produced. (c) The block is now lowered to a greater depth. What effect, if any, does this have on the tension in the cable? Justify your answer.
1996 Q2 A child on a sledge slides down a slope which is at an angle of 20º to the horizontal as shown below. The combined weight of the child and the sledge is 400 N. The frictional force acting on the sledge and child at the start of the slide is 20.0 N. (a) (i) Calculate the component of the combined weight of the child and sledge down the slope. (ii) Calculate the initial acceleration of the sledge and child. (b) The child decides to start the slide from further up the slope. Explain whether or not this has any effect on the initial acceleration. (c) During the slide, the sledge does not continue to accelerate but reaches a constant speed. Explain why this happens.
1994 Q2 (a) A hot air balloon, of total mass 500 kg, is held stationary by a single vertical rope. (i) Draw a sketch of the balloon. On your sketch, mark and label all the forces acting on the balloon. (ii) When the rope is released, the balloon initially accelerates vertically upwards at 1.5 ms -2. Find the magnitude of the buoyancy force. (iii) Calculate the tension in the rope before it is released. (b) An identical balloon is moored using two ropes, each of which makes an angle of 25º to the vertical, as shown below. By using a scale diagram, or otherwise, calculate the tension in each rope. (c) During a flight, when a hot air balloon is travelling vertically upwards with constant velocity, some hot air is released. This allows cooler air to enter through the bottom of the balloon. Describe and explain the effect of this on the motion of the balloon. You may assume that the volume of the balloon does not change.
1991 Q3 A sonar detector, of mass 60 kg, is used for monitoring the presence of dolphins. It is attached by a vertical cable to the sea bed so that the detector is held below the surface of the sea. (a) Explain the cause of the buoyancy force on the detector. (b) Draw a diagram showing the buoyancy force and the other forces acting on the detector. (c) If the buoyancy force has a value of 31500 N, what is the value of the tension in the cable attached to the sea bed? (d) The detector is now used at the same depth in fresh 'water. How would this affect the value of the buoyancy force? Justify your answer. [DATA:- Density of water = 1000 kgm -3, Density of sea water = 1020 kgm -3 ]
1998 Q1 A trolley of mass 2.0 kg is catapulted up a slope. The slope is at an angle of 20º to the horizontal as shown in the diagram below. The speed of the trolley when it loses contact with the catapult is 3.0 ms -1. The size of the force of friction acting on the trolley as it moves up the slope is 1.3 N. (a) (i) Calculate the component of the weight of the trolley acting parallel to the slope. (ii) Draw a diagram to show the forces acting on the trolley as it moves up the slope and is no longer in contact with the catapult. Show only forces or components of forces acting parallel to the slope. Name the forces. (iii) Show that, as the trolley moves up the slope, it has a deceleration of magnitude 4.0 ms -2. (iv) Calculate the time taken for the trolley to reach its furthest point up the slope. (v) Calculate the maximum distance the trolley travels along the slope. The trolley now moves back down the slope. (b) (i) Draw a diagram to show the forces acting on the trolley as it moves down the slope. Show only forces or components of forces acting parallel to the slope. Name the forces. (ii) The magnitude of the deceleration of the trolley is 4.0 ms -2 as it moves up the slope. Explain why the magnitude of the acceleration is not 4.0 m s -2 when the trolley moves down the slope
1998 Q2 A student performs an experiment to study the motion of the school lift as it moves upwards. The student stands on bathroom scales during the lift's journey upwards. The student records the reading on the scales at different parts of the lift's journey as follows. (a) Show that the mass of the student is 60 kg. (b) Calculate the initial acceleration of the lift. (c) Calculate the deceleration of the lift. (d) During the journey, the lift accelerates for 1.0 s, moves at a steady speed for 3.0 s and decelerates for a further 1.0 s before coming to rest. Sketch the acceleration-time graph for this journey.
1999 Q2 A bungee jumper is attached to a high bridge by a thick elastic rope as shown. The graph shows how the velocity of the bungee jumper varies with time during the first 6 seconds of a jump. The mass of the bungee jumper is 55 kg. (a) Using the information on the graph, state the time at which the bungee rope is at its maximum length. Justify your answer. (b) Calculate the average unbalanced force, in newtons, acting on the bungee jumper between the points A and B on the graph. (c) Explain, in terms of the force of the rope on the bungee jumper, why an elastic rope is used rather than a rope that cannot stretch very much.
2000 Q3(a) A rocket is used to launch a spacecraft. (a) The rocket and spacecraft have a combined mass of 3.0 x 10 5 kg. On lift-off from the Earth, the rocket motors produce a force of 3.6 x 10 6 N. (i) Draw a diagram of the rocket to show the forces acting on the rocket just after lift-off. You must name each force. (ii) Calculate the initial acceleration of the rocket. (iii) Although the force exerted by the rocket motors remains constant, the acceleration of the rocket increases as the rocket rises. Give one reason why this happens.
2001 Q4(b) (b) During a dive, a cannon is found. A cable from a crane on a barge is attached to the cannon. The cannon is raised slowly from the seabed at constant speed. The weight of the cannon is 20.0 kn. At A, 40 m below the surface, the tension in the cable is 17.5 kn. The weight of the cable and any friction caused by the water may be neglected. (i) At A, the tension in the cable is less than the weight of the cannon. Name the other force acting on the cannon and state its value. (ii) What is the size of the tension in the cable when the cannon is at B, 30 m below the surface? (iii) What is the size of the tension in the cable when the cannon is at rest at C, above the surface of the sea?