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 w

Question

3 years ago

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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 w

ith k = 3 × 103 N/m. The block slides down the ramp and compresses the spring. Find the maximum compression of the spring.

Physics

2 answers:

irinina [24] · Answer 1 · 2022-02-21T13:51:13+03:00

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

Serjik [45] · Answer 2 · 2022-02-21T15:27:20+03:00

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.

Please see the attachment below for the full solution.