3) A ramp making an angle of = 30.0° with the horizontal is against a wall. A ma

Question

3) A ramp making an angle of = 30.0° with the horizontal is against a wall. A mass of m = 20.0 kg is on the ramp, and is attached to the wall by a spring whose equlibrium length is L 1.20 m, and whose spring constant is k- 900. N/m. The static coefficient of friction between the mass and the ramp is is 0.800. The spring is initially unstretched. The mass is then pulled further down the ramp by an additional 0.600 m, and let go. What is the maximum possible range of positions (as measured from the wall, along the ramp) at which the mass eventually comes to rest? Figure 3-A ramp making an angle of 30.0° with the horizontal is against a wall. A mass of m-20.0 kg is on the ramp, and is attached to the wall by a spring whose equlibrium length is L = 1.20 m, and whose spring constant is k-900. N/m. The static coefficient of friction between the mass and the ramp is As-0.800

Explanation / Answer

3. theta = 30 deg

m = 20 kg

L = 1.2 m

k = 900 N/m

coefficnet of static friciton mus = 0.8

the mass will come to rest when extension is x

then

kx = mgsin(theta) + mus*mgcos(theta)

900*x = 20*9.81(sin(30) + 0.8cos(30))

x = 0.26 m

hence distance form the wall = L + x = 1.46 m

for a compression x

kx + mgsin(theta) = mus*mgcos(theta)

900*x = 20*9.81(0.8cos(30) - sin(30))

x = 0.042 m

distance from wall = L - x = 1.157 m

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