The motor, M, pulls on the cable with a force F = (10t2 + 300) N, where t is in seconds. If the 100 kg crate is originally at rest at t = 0, determine its speed when t = 4 s. Neglect the mass of the cable and pulleys and there is no friction between the box and walls. Hint: First find the time needed to begin lifting the crate.

Question

Antoine Martin

Physics

Today, 07:34

The motor, M, pulls on the cable with a force F = (10t2 + 300) N, where t is in seconds. If the 100 kg crate is originally at rest at t = 0, determine its speed when t = 4 s. Neglect the mass of the cable and pulleys and there is no friction between the box and walls. Hint: First find the time needed to begin lifting the crate.

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Israel · Answer 1

14.13 m/s

Explanation:

Parameters given:

Mass, m = 100 kg

F = 10t² + 300

We know that force is given as:

F = m * a

=> ma = 10t² + 300

Where a = acceleration

Given that mass, m = 100:

=> a = (10/100) t² + (300/100)

a = 0.1t² + 3

To find the velocity, we integrate acceleration, a:

a = dv/dt = 0.1t² + 3

v = (0.1/3) t³ + 3t

When t = 4 secs:

v = (0.1 * 4³) / 3 + (3 * 4)

v = 2.13 + 12

v = 14.13 m/s