Question

ramp, which makes an angle of 30o degrees to the horizontal. A distance d = 1.3 m away from the block is an unstretched spring with k = 3 × 103 N/m. The block slides down the ramp and compresses the spring. Find the maximum compression of the spring.

Answer 1

Answer:

The maximum compression of the spring is 0.154 m

Explanation:

From the energy theorem, we have that the net work equals the change in kinetic energy. If x is the vertical height that the block slides when compressed by a spring, we have to:

m*g*(d + x)*sin*(30°) - 0.5*k*x^2 = 0

This equation equals zero because there is no change in block speed. Replacing values:

5*9.8*(1.3+x)*0.5 = 0.5*3000*x^2

24.5*(1.3+x) = 1500*x^2

1500*x^2 - 24.5*x - 31.9 = 0

solving this quadratic equation we have that x = 0.154 m

Answer 2

Answer:

X = 0.146m

Explanation:

Mass = 5kg

Given k= 3×10³ N/m

d = 1.3m

theta = 30°

h = dSin30° = 0.65m

The gravitational potential energy at the top of the ram is converted to the elastic potential energy at the bottom the ramp where the spring is located.

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