The displacement of a particle is shown in the displacement-time graph below. Displacement is measured in metres from its starting position and time is measured in seconds.
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The displacement of a particle is shown in the displacement-time graph below. Displacement is measured in metres from its starting position and time is measured in seconds.
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Two spheres and are of equal radius and have masses and respectively. and are moving in the same direction in a straight line on a smooth horizontal surface when they collide directly. Immediately before the collision, and are moving with speeds and respectively. Immediately after the collision, the speed of is , the speed of is and the direction of motion of is unchanged.
Find the two possible values of .
Show that the minimum total kinetic energy lost in the collision is
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The following force diagram shows three forces acting on a particle:
Given that the resultant force on the particle in the vertical direction is 44.8 N downwards, find the size of the angle . Give your answer in degrees correct to 3 significant figures.
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A particle of mass 12 kg is being pushed up a smooth slope by a force of 50 N that acts horizontally. The slope is inclined at 20° to the horizontal, as shown in the diagram below:
Calculate the acceleration of the particle up the slope.
Calculate the normal reaction force of the slope on the particle.
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A train consisting of an engine and five carriages moves forwards on a straight horizontal track. The couplings that connect the carriages can be modelled as light and inextensible. A constant resistive force of 2800 N acts on the engine and a constant resistive force of 500 N acts on each of the five carriages. The maximum speed of the train on the track is 35 m s-1.
Find the maximum power output of the engine.
Find the maximum acceleration of the train at the instant when it is travelling at a speed of 20 m s-1. The mass of the engine is 15 tonnes, and the mass of each carriage is 7 tonnes.
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A home-made rocket is launched from rest at ground level with time .
The acceleration of the rocket, measured in metres per square second, is modelled by the equation
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A particle moving along a straight line has velocity , at time t seconds, and its motion is described the equation
v = t2 − 4t + 4
Show that the acceleration of the particle is negative for the first 2 seconds of its motion.
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Two particles A and B, of masses 2.7 kg and 2.2 kg respectively, are connected by means of a light inextensible string. Particle A is held motionless on a rough fixed plane inclined at 25° to the horizontal. The string passes over a smooth light pulley fixed at the top of the plane so that B is hanging vertically downwards as shown in the diagram below:
The string between A and the pulley lies along a line of greatest slope of the plane, and B hangs freely from the pulley. The coefficient of friction between particle A and the plane is μ.
The system is released from rest with the string taut. Given that particle B descends 1.82 m in the first 3 seconds after it is released, find the value of μ.
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