You are an industrial engineer with a shipping company. As part of the package- handling system, a small box with mass 1.60 kg i

Question

3 months ago

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You are an industrial engineer with a shipping company. As part of the package- handling system, a small box with mass 1.60 kg i

s placed against a light spring that is compressed 0.280 m. The spring has force constant 48.0 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 μk = 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. (a) What is the speed of the box at the instant when it leaves the spring? (b) What is the maximum speed of the box during its motion?

Physics

1 answer:

ValentinkaMS [3.4K] · Answer 1 · 2026-02-21T16:17:45+03:00

Answer:

a) V = 0.82m/s

b) Vmax = 0.985 m/s

Explanation:

According to the conservation of energy, we know:

Eo = Ef $\frac{m*V^{2}}{2}-\frac{K*Xmax^{2}}{2}=-Ff*Xmax$

We find V by solving this:

V = 0.82 m/s

To calculate the maximum speed, we will also solve for an intermediate position where compression is X, and the work done by friction is given as (Xmax - X) = (0.28m - X):

$\frac{m*Vmax^{2}}{2}+\frac{K*X^{2}}{2}-\frac{K*Xmax^{2}}{2}=-Ff*(Xmax-X)$

We will then differentiate and set the result to zero to find position X. After performing the derivative, we discover:

X = 0.1m Putting this back into the equation for Vmax:

Vmax = 0.985m/s