Physics Review Question Unit: mechanics Year: 1995 Question#: 14 Question: In the diagram below, a 0.4-kilogram steel sphere and a 0.1-kilogram wooden sphere are located 2.0 meters above the ground. Both spheres are allowed to fall from rest. Which statement best describes the spheres after they have fallen 1.0 meter? [neglect air resistance.] (1 ) Both spheres have the same speed and momentum. (2 ) Both spheres have the same speed and the steel sphere has more momentum than the wooden sphere. (3 ) The steel sphere has greater speed and has less momentum that the wooden sphere. (4 ) The steel sphere has greater speed than the wooden sphere and both spheres have the same momentum. What is this question really asking? Explanation by: Gabrielle [ Return to question menu ] Answer 1 Both spheres have the same speed and momentum INCORRECT Use the formula Vf2=Vi2 + 2a s to figure out the speed of the objects. You will find that the speed of the steel ball and the speed of the wood ball are equal. To find the momentum use the formula p=mv. You will find that the momentums are not the same. return to top Answer 2 Both spheres have the same speed and the steel sphere has more momentum than the wooden sphere. CORRECT Use the formula Vf2 = Vi2 + 2a s to find the speed of the objects. Vi= 0m/s, a=9.8m/ss, s=1m. Vf2=0m/s2+2(9.8m/ss)(1m)= m/s. The objects have the same velocity because no conditions of the formula differ. To find the momentum use the formula p=mv. For the steel ball mass=.4kg and the velocity=m/s. P=(.4kg)(m/s). P=1.7kg*m/s. For the wood ball mass=.1 kg, velocity=m/s. P=(.1kg)(m/s). P=.44Kg*m/s. The momentum of the steel ball is greater than that of the wood ball. They have the same speed but different momentums. return to top Answer 3 The steel sphere has greater speed and has less momentum that the wooden sphere. INCORRECT The two balls have the same speed and the steel ball has more momentum than the wooden ball. return to top Answer 4 The steel sphere has greater speed than the wooden sphere and both spheres have the same momentum. INCORRECT Ignoring air friction, all objects fall at the same rate (acceleration due to gravity) so the speed of the objects both dropped at the same time could not be different. The momentum (p=mv) would be different for each because the mass is different. return to top What's this question really asking? This question is really asking under what conditions are the momentums of two different objects different (when the mass is different and/or the velocity) and without air resistance are the speeds of two objects the same. return to top
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