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 1.20 kg is placed against a light spring that is compressed 0.280 m. The spring has force constant 42.0 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?

Express your answer with the appropriate units

Part B

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

Express your answer with the appropriate units.

Explanation / Answer

Here,

m = 1.20 Kg

compression , x = 0.280 m

spring constant , k = 42 N/m

uk = 0.300

part A)

let the speed of the box is v

Using conservation of energy

0.5 * m * v^2 = 0.5 * k * x^2 - uk * m * g * x

0.5 * 1.20 * v^2 = 0.5 * 42 * 0.280^2 - 0.3 * 1.20 * 9.8 * 0.280

solving for x

x = 1.05 m/s

the speed of block is 1.05 m/s

b) for the maximum speed of the box

u * m * g - k * x = 0

0.3 * 9.8 * 1.20 - 42 * x =0

x = 0.084 m

0.5 * m * v^2 = 0.5 * k * (x2^2 - x1^2) - uk * m * g * x

0.5 * 1.20 * v^2 = 0.5 * 42 * (0.280^2 - 0.084^2) - 0.3 * 1.20 * 9.8 * (0.280 - 0.084)

solving for v

v = 1.16 m/s

the maximum speed of the box is 1.16 m/s

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