A 4 kg block is launched up a frictionless inclined plane by a spring as shown i

Question

A 4 kg block is launched up a frictionless inclined plane by a spring as shown in the figure below. The plane is inclined at 30? and the spring constant is 800 N/m . The block is initially pushed against the spring in order to compress the spring 0.20 m , and then it is released.

Part A

Calculate the magnitude of the acceleration of the block the moment after it is released.

Part B

Calculate the acceleration when the spring reaches the point where its compression is 0.07 m .

Part C

What is the magnitude of the acceleration when the spring reaches the point where its compression is zero?

Problem 5.57 A 4 kg block is launched up a frictionless inclined plane by a spring as shown in the figure below. The plane is inclined at 30° and the spring constant is 800 N/m. The block is initially pushed against the spring in order to compress the spring 0.20 m, and then it is released. 30°

Explanation / Answer

A)

Along the incline using F = ma

kx - mgsin30 = ma

(800 x 0.20) - (4 x 9.81 x sin30) = 4 a

a = 35.10 m/s^2 upwards

B)

kx - mgsin30 = ma

(800 x 0.07) - (4 x 9.81 x sin30) = 4 a

a = 9.10 m/s^2 upwards

C) mgsin30 =ma

a = 9.81 x sin30 =4.91 m/s^2 downwrads

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