work and kepler's law

2009-10-12 10:12 am

1.A car of mass m accelerates from speed v_1 to speed v_2 while going up a slope that makes an angle theta with the horizontal. The coefficient of static friction is u_s, and the acceleration due to gravity is g. Find the total work W done on the car by the external forces.
Express your answer in terms of the given quantities. You may or may not use all of them.

2.A Ferris wheel 21.0 m in diameter rotates once every 22.0 s.
What is the ratio of a person's apparent weight to her real weight at the top?
What is the ratio of a person's apparent weight to her real weight at the bottom?

回答 (1)

Prof. Physics

2009-10-12 5:47 pm

✔ 最佳答案

1. Note that the applied force, the weight and the frictional force are all external forces on the car.

So, the total work done W on the car by all the external forces are used to increase the kinetic energy of the car.

W = 1/2 m(v22 - v12)

2. Angular speed, w = 2pi / T = 2pi / 22.0 = pi/11 rads-1

The reaction force acting on the person is actually his/her apparent weight.

At the top, mg - N = mrw2

N = mg - mrw2 = m(10 - (21/2)(pi/11)2) = 9.144m

So, the ratio = N/mg = 9.144/10 = 0.914

At the bottom, N - mg = mrw2

N = mg + mrw2 = m(10 + (21/2)(pi/11)2) = 10.856m

So, the ratio = N/mg = 10.856/10 = 1.086

參考: Physics king

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