Question

A 75-N crate rests in a perfectly smooth ice arena. The minimum force needed ti start the box moving is...

Answer 1

The minimum force needed to start the 75-N crate moving on the perfectly smooth ice arena is 75 Newtons.

Step-by-step explanation:

On a perfectly smooth surface like ice, the force required to overcome static friction and initiate motion is equal to the maximum static friction force. The force of static friction
`(\(F_{\text{static}}\))` can be calculated using the formula
`\(F_{\text{static}} = \mu_s * N\),` where
`\(\mu_s\)` is the coefficient of static friction and N is the normal force. However, in this scenario, the crate is on a perfectly smooth surface, meaning there is no friction to overcome. Thus, the force required to start the crate moving is solely determined by its weight, which is given as 75 Newtons.

On a surface with friction, the force needed to overcome static friction would depend on the coefficient of static friction and the normal force exerted by the surface. However, in the case of a perfectly smooth ice arena, the absence of frictional forces means that the crate will begin to move as soon as a force equal to its weight is applied in any direction.

This is due to the absence of opposing forces that would otherwise impede its motion. Therefore, the minimum force required to initiate movement for this crate on the smooth ice surface is its weight of 75 Newtons.