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

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