You are an industrial engineer with a shipping company. As part of the package-h

Question

You are an industrial engineer with a shipping company. As part of the package-handling system, a small box with mass 1.60 kg is placed against a light spring that is compressed 0.280 m. The spring has force constant 45.0 N/m . The spring and box are released from rest, and the box travels along a horizontal surface for which the coefficient of kinetic friction with the box is ?k = 0.300. When the box has traveled 0.280 m and the spring has reached its equilibrium length, the box loses contact with the spring.

Part A

What is the speed of the box at the instant when it leaves the spring?

Part B

What is the maximum speed of the box during its motion?

Explanation / Answer

(A) Applying energy conservation,

Work done by friction + work done by spring = change in KE

(- uk m g d) + (k d^2 / 2) = m v^2 /2 - 0

-(2 x 0.3 x 1.60 x 9.8 x 0.280) + (45 x 0.280^2) = 1.60 v^2

v = 0.75 m/s ....Ans

(B) max speed will be at equilibrium position,

k x = uk m g

45 x = (0.30)(1.60)(9.80)

x = 0.105 m

Applying energy conservation again,

(-0.3 x 1.60 x 9.8 x 0.105) + (45 x (0.280^2 - 0.105^2) /2) = 1.60 v^2 / 2

v = 1.13 m/s

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