Phys 195, Quiz 5 Ch. 7-8 Name: 1. The gravitational force exerted by the Sun on

Question

Phys 195, Quiz 5 Ch. 7-8 Name: 1. The gravitational force exerted by the Sun on the Earth causes the Earth to orbit about the Sun. Assume that the orbit is perfectly circular. The work done by this gravitational force during a small displacement of the Earth along is orbital path is (a) zero (b) positive (c) negative (d) impossible to determine. 2. The figure shows four examples of a force applied to an object. In all cases, the force has the same magnitude, and the displacement of the object is to the right and of the same magnitude. Rank the situations in order of the work done by the force from most positive to negative: . A dart is inserted into a spring-loaded dart gun by compressing the spring in by a distance x. For the next loading, the spring is compressed a distance 2x. How much work is required to load the second dart compared with the first? (a) four times as much (b) twice (c) the same (d) one-half (e) one-quarter How much faster does the second dart leave the gun compared with the first? a) four times as fast (b) two times (c) the same (d) one-half (c) one-quarter 4 Choose the correct answer. The gravitational potential energy of a system be negative or positive mark which of the following statements about the particle (a) is always positive (b) is always negative (c) can s. If the net work done by external forces on a particle is zero, must be true (a) Its velocity is zero (b) Its velocity is decreased (c) Its velocity is unchanged (d) Its speed is unchanged (e) More information is needed

Explanation / Answer

3.

for first dart :

W1 = (0.5) k x2

for second dart :

W2 = (0.5) k (2x)2 = 4 (0.5) k x2 = 4 W1

hence 4 times as much choice a)

using conservation of energy for dart 1

(0.5) k x2 = (0.5) m v12

v1 = sqrt(k/m)x

using conservation of energy for dart 2

(0.5) k (2x)2 = (0.5) m v12

v2 = 2 sqrt(k/m) x = 2 v1

hence b ) two times

4 b)

U = - G M m/r

5 d)

W = (0.5) m (vf2 - vi2)

if W = 0

vf = vi

6 b)

dU/dx = - F

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