A $45.0$-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds $313$ N. Then you must reduce your push to $208$ N to keep it moving at a steady $25.0$ cm/s. Suppose you were performing the same experiment on the moon, where the acceleration due to gravity is $1.62$ m/s².
(i) What magnitude push would cause it to move?
(ii) What would its acceleration be if you maintained the push in part (b)? Note: Part (b) asked what push you must exert to give it an acceleration of $1.10$ m/s².

A pickup truck is carrying a toolbox, but the rear gate of the truck is missing. The toolbox will slide out if it is set moving. The coefficients of kinetic friction and static friction between the box and the level bed of the truck are $0.355$ and $0.650$, respectively. Starting from rest, what is the shortest time this truck could accelerate uniformly to $30.0$ m/s without causing the box to slide? Draw a free-body diagram of the toolbox.

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$, and the coefficient of kinetic friction is $0.20$. If the monkey applies a horizontal force of $18.0$ N, what is the magnitude of the friction force and what is the box's acceleration?

Two crates connected by a rope lie on a horizontal surface (Fig. E$5.37$). Crate A has mass $m_A$, and crate B has mass $m_B$. The coefficient of kinetic friction between each crate and the surface is ${\mu }_k$. The crates are pulled to the right at constant velocity by a horizontal force $F$. Draw one or more free-body diagrams to calculate the following in terms of $m_A$, $m_B$, and ${\mu }_k$: the magnitude of $F$.

A $25.0$-kg box of textbooks rests on a loading ramp that makes an angle $\alpha$ with the horizontal. The coefficient of kinetic friction is $0.25$, and the coefficient of static friction is $0.35$. At this angle, find the acceleration once the box has begun to move.

A $45.0$-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds $313$ N. Then you must reduce your push to $208$ N to keep it moving at a steady $25.0$ cm/s. What push must you exert to give it an acceleration of $1.10$ m/s²?

A $45.0$-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds $313$ N. Then you must reduce your push to $208$ N to keep it moving at a steady $25.0$ cm/s. What are the coefficients of static and kinetic friction between the crate and the floor?