23 A 50 kg bucket of water is raised from a well by a rope If the upward

# 23 a 50 kg bucket of water is raised from a well by a

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23. A 5.0-kg bucket of water is raised from a well by a rope. If the upward acceleration of the bucket is 3.0 m/s 2 , fi nd the force exerted by the rope on the bucket. 24. A shopper in a supermarket pushes a loaded cart with a hor- izontal force of 10 N. The cart has a mass of 30 kg. (a) How far will it move in 3.0 s, starting from rest? (Ignore friction.) (b) How far will it move in 3.0 s if the shopper places his 30-N child in the cart before he begins to push it? 25.A 2 000-kg car is slowed down uniformly from 20.0 m/s to5.00 m/s in 4.00 s. (a) What average force acted on thecar during that time, and (b) how far did the car travelduring that time? 26. Two packing crates of masses 10.0 kg and 5.00 kg are con- nected by a light string that passes over a frictionless pul- ley as in Figure P4.26. The 5.00-kg crate lies on a smooth incline of angle 40.0 . Find the acceleration of the 5.00-kg crate and the tension in the string. 28.An object of mass 2.0 kg starts from rest and slides downan inclined plane 80 cm long in 0.50 s. What net forceisacting on the object along the incline? 29.A 40.0-kg wagon is towed up a hill inclined at 18.5withrespect to the horizontal. The tow rope is parallel to theincline and has a tension of 140 N. Assume that thewagon starts from rest at the bottom of the hill, andneglect friction. How fast is the wagon going after moving80.0 m up the hill? 30. An object with mass m 1 5.00 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m 2 10.0 kg, as shown in Figure P4.30. Find the ac- celeration of each object and the tension in the cable. 27. Assume that the three blocks portrayed in Figure P4.27 move on a frictionless surface and that a 42-N force acts as shown on the 3.0-kg block. Determine (a) the accel- eration given this system, (b) the tension in the cord connecting the 3.0-kg and the 1.0-kg blocks, and (c) the force exerted by the 1.0-kg block on the 2.0-kg block. 31. A train has a mass of 5.22 10 6 kg and is moving at 90.0 km/h. The engineer applies the brakes, resulting in a net backward force of 1.87 10 6 N on the train. The brakes are held on for 30.0 s. (a) What is the fi nal speed of the train? (b) How far does the train travel during this period? 32. (a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater, T or w ? (b) When the elevator is moving at a constant velocity upward, which is greater, T or w ? (c) When the elevator is moving upward, but the acceleration is downward, which is greater, T or w ? (d) Let the elevator have a mass of 1 500 kg and an upward acceleration of 2.5 m/s 2 . Find T . Is your answer consistent with the answer to part (a)? (e) The elevator of part (d) now moves with a constant up- ward velocity of 10 m/s. Find T . Is your answer consistent with your answer to part (b)? (f) Having initially moved upward with a constant velocity, the elevator begins to ac- celerate downward at 1.50 m/s 2 . Find T . Is your answer consistent with your answer to part (c)?
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