You throw a baseball straight upward. The drag force is proportional to $v^2$. In terms of $g$, what is the $y$-component of the ball's acceleration when the ball's speed is half its terminal speed and it is moving up?

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 $μ_k$. 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 $μ_k$: the tension in the rope connecting the blocks.

A $52$-kg ice skater spins about a vertical axis through her body with her arms horizontally outstretched; she makes $2.0$ turns each second. The distance from one hand to the other is $1.50$ m. Biometric measurements indicate that each hand typically makes up about $1.25\%$ of body weight. What horizontal force must her wrist exert on her hand?

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 $F$.

You throw a baseball straight upward. The drag force is proportional to $v^2$. In terms of $g$, what is the $y$-component of the ball's acceleration when the ball's speed is half its terminal speed and it is moving back down?

A small remote-controlled car with mass $1.60$ kg moves at a constant speed of $v=12.0$ m/s in a track formed by a vertical circle inside a hollow metal cylinder that has a radius of $5.00$ m (Fig. E$5.45$). What is the magnitude of the normal force exerted on the car by the walls of the cylinder at point $A$ (bottom of the track)?

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.