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Mechanics Revision AJC P2 Q2 2 (a) Use Newton’s laws of motion to explain why an object moving with uniform speed in a circle must experience a force towards the centre of the circle. (b) An aircraft of mass 5.0 × 104 kg moves with a constant speed of 0.20 km s-1 in a horizontal circle of radius 15 km. (i) Show on a sketch the forces acting on the aircraft in the vertical plane containing the aircraft and the centre of the circle. (ii) Find the magnitude and direction of the resultant force. Mechanics Revision VJC P2 Q2 2 Using a rope, a bucket of water is swung in a vertical circle of radius 0.950 m. The mass of the water and bucket is 3.25 kg. At the top of the circle, the speed of the bucket is 3.23 m s-1 and the bucket is upside down at this instant. (a) What is the tension in the rope tied to the bucket at the top of the circle? (b) Explain qualitatively why the water in the bucket does not fall out. (c) What is the magnitude and direction of the force acting on the water by the bucket when it is at the top? Take the mass of water to be 2.25 kg. Mechanics Revision MJC P2 Q1 1 A car, on a steep incline of 37.0° below the horizontal, rolls down from rest with a constant acceleration of 4.00 m s-2 along the incline. It travels 50.0 m down to the edge of a vertical cliff, which is 30.0 m above the ocean surface as shown in Fig 1.1. Find (a) the speed of the car when it reaches the edge of the cliff and the time it takes to get there. (b) the velocity, v of the car when it lands in the ocean. (c) the total time, t that the car takes to move from point A to C. Mechanics Revision RJC P2 Q2 2 When serving a ball, a tennis player first throws the ball vertically upwards with one hand and hit the ball at the highest point with his racket in the other hand. (a) When the ball is in contact with the racket, a force of 70 N is exerted on the ball at right angle to the surface of the racket. The ball leaves the surface of the racket perpendicularly with speed 50 m s-1, making an angle of 8.0° to the horizontal as shown in Fig 2. below. (i) Calculate the length of time the ball is in contact with the racket surface given that the ball has a mass of 0.060 kg. (ii) The ball was hit by a racket at the highest point of its motion which was 3.2 m above the ground. Given that the net was 1.0 m high and the player was 11.5 m away from the net, how high above the net was the ball when it passed over the net? Neglect air resistance. (b) If the opponent’s reaction is 0.30 s from the time he sees the player hit the ball and runs at a speed of 3.0 m s-2 in a straight line parallel to the vertical plane of the trajectory of the ball, calculate the distance the opponent would have run when the ball first touches his side of the court.