hw5_sp10_sol - Physics 101 Classical Physics Spring 2010...

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Physics 101 Classical Physics Spring 2010 Homework 5 Solutions DUE IN CLASS ON FEBRUARY 25 1. If a moving object halves its speed, its kinetic energy: (a) increases by a factor of 2 (b) decreases by a factor of 2 (c) increases by a factor of 4 (d) decreases by a factor of 4 (e) remains the same Since kinetic energy is proportional to speed squared, if the speed is halved, the kinetic energy decreases by a factor of 4. 2. In which of the following examples is work done? (a) A weightlifter holds a 1000 lb barbell above his head (b) A man rubs his hands together and they get warm (c) A 60 kg boy leans against a wall at a 45 angle (d) The moon orbits the Earth (e) A pot of water sits over a fire until it boils While the man’s hands are rubbed together, friction is in the opposite direction of the displacement, so work is done. For (a), (c), and (e), there is zero diplacement and therefore zero work done. In the case of the moon orbiting the earth, the force due to gravity acts perpendicular to the displacement, so there is no work done. 3. A student weighing 130 lbs walks up 100 steps, each 10 cm in height. What is the minimum number of calories burned off in this exercise? Keep in mind that the calories we speak about in fitness are really kilocalories, and that there are 4.184 Joules in a real calorie. (a) 1300, (b) 25, (c) 6, (d) 1.4 , (e) 2470 W = ~ F · Δ x = (130 lb) 4 . 448 N 1 lb (100 * 0 . 1 m) 1 kcal 4184 J = 1 . 4 Cal 4. A force F acts on a block for a time t . Assume the block has an initial velocity v . Initial velocity in which direction would result in the greatest amount of work done on the block? (a) Initial velocity to the left (b) Initial velocity to the right (c) Initial velocity in either direction would result in the same amount of work done because the distance traveled would be the same. (e) Initial velocity in either direction would result in the same amount of done because the time t is constant. (e) None of the above. 1
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The greatest amount of work is done when the intitial velocity is in the direction of the force. This is because the force will increase the speed of the block in that case, and the block will then travel a larger distance in the time t than if the velocity were in the opposite direction of the force. It was intended that the force act to the right, but since it was not explicitly specified, credit was given for any answer. 5. The weight of an object on the Moon is 1/6 that of its weight on the Earth. The ratio of kinetic energy of a body on Earth moving with speed v to that of the same body moving with the same speed v on the Moon is: (a) 6:1, (b) 36:1, (c) 1:6, (d) 1:36, (e) 1:1 The kinetic energy of the object is T = mv 2 / 2 where m is the mass not the weight. The weight is reduced not because the mass is reduced but rather because g is reduced by a factor of 6. Therefore, the kinetic energy is the same as on earth.
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