If the motor exerts a force of F = (600 + 2s2) N on the cable, determine the speed of the 100-kg crate when it rises to s = 15 m. The crate is initially at rest on the ground.

The motor that exerts force is F = 600+2s²

Mass of crate is m = 100kg

Distance raises is s = 15m

Crate at rest is V₁ = 0

We will solve this using principle of energy and work because involves displacement, velocity, and force

Work energy is

T₁ + ΣU₁₋₂ = T₂

Whereby T₁ = initial Kinetic energy

= 1/2mw₁² = 1/2m (o) ₁² = 0 Because initial is at rest.

Motor exerts the force on the cable forces acting in the cable at C are two times motor exerts force cable M work done by the exerted motor is

U₁₋₂ = 2∫s²Fds

U₁₋₂ = 2∫s² (600+2S²) ds

=2 (600*s + 2s³/3) ¹⁵

= 2 (600 * 15 + 2 * 15³/3)

=22500N

Work done by crate is the crates' weight acts downward to take the negative sign

U₁₋₂ = - (m * g * s)

U₁₋₂ = - (100 * 9.81 * 15)

= - 14715N

T₂ = Final kinetic energy = 1/2mw²₂

T₁ + ∑U₁₋₂ = T₂

0 + (22500 + (-14715)) = 1/2 (100) V²₂

V₂ = 12.47m/s