21. A spring requires a force of 5.0 N to compress it 0.1 m. How much work (in j

Question

21. A spring requires a force of 5.0 N to compress it 0.1 m. How much work (in joules) is required to stretch the spring 0.4 m? A) 15 B) 20 C) 4 D) 8 E) None of these 22. A spring with constant k = 278 N/m is at the base of a frictionless, 30.0 degree -inclined plane, 1.1 meters long. A 0.50-kg block is pressed against the spring, compressing it 0.20 m from its equilibrium position. The block is then released. What will be its speed (in m/s) when it reaches the top of the ramp? 2.6 2.8 3.0 3.4 None of these 23. A 0.750-kg object is oscillating vertically at the end of a spring whose spring constant is 2875 N/m. About how many oscillations will the object make in one minute, assuming air resistance is ignorable? (Note: omega^2 = k/m.) 80 170 380 480 None of these

Explanation / Answer

21) F = k x

5 = k *0.1

k = 50 N/m

W = 1/2 k x^2 = 0.5*50*0.4^2= 4 J

so C)

22)

Ei = Ef

1/2 kx^2 = 1/2 mv^2 + m g h

0.5*278*0.2^2 = 0.5*0.5*v^2 + 0.5*9.81*1.1*sin(30 degrees)

v=3.38 m/s so D)

23)

w = sqrt(k/m) = sqrt( 2875/0.75)= 61.9

w = 2 pi f

f = 61.9/(2*pi)= 9.85 Hz

so number oscillation = 60*9.85= 590
so none of these E)

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