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If the motor exerts a force of f = (600 2s2) n on the cable, determine the speed of the 137-kg crate when it rises to s = 15 m. the crate is initially at rest on the ground

Answer :

The speed of the 137-kg crate when it rises to a height of 15 m, with an initial rest, can be determined using the given force exerted by the motor. To find the speed of the crate, we can apply the work-energy principle. The work done by the motor is equal to the change in the crate's kinetic energy.

The work done by a force is given by the equation W = F * d * cosθ, where W is the work done, F is the force applied, d is the displacement, and θ is the angle between the force and displacement vectors. In this case, the force exerted by the motor is given as f = (600 2s^2) N, and the displacement is s = 15 m. Since the crate starts from rest, its initial kinetic energy is zero. Thus, the work done by the motor is equal to the final kinetic energy.

Using the equation W = (1/2) * m * v^2, where m is the mass of the crate and v is its final velocity, we can solve for v. Rearranging the equation, we have v = √(2W/m). Substituting the given values, we can calculate the work done by the motor and the final velocity of the crate when it reaches a height of 15 m.

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The correct question is -

What is the speed of the 137-kg crate when it rises to a height of 15 m, given that the motor exerts a force of f = (600 - 2s^2) N on the cable and the crate is initially at rest on the ground?

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