The sports car, having a mass of $1700 \mathrm{~kg}$, travels horizontally along a $20^{\circ}$ banked track which is circular and has a radius of curvature of $\rho=100 \mathrm{~m}$. If the coefficient of static friction between the tires and the road is $\mu_s=0.2$, determine the maximum constant speed at which the car can travel without sliding up the slope. Neglect the size of the car.

The acceleration of a package sliding at point $A$ is $3 \mathrm{~m} / \mathrm{s}^2$. Assuming that the coefficient of kinetic friction is the same for each section, determine the acceleration of the package at point $B$.

At the instant shown, cars A and B travel at speeds of 70 mi / h and 50 mi / h, respectively. If B is increasing its speed by $1100 mi / h ^2$, while A maintains a constant speed, determine the velocity and acceleration of B with respect to A. Car B moves along a curve having a radius of curvature of 0.7 mi.

A hockey player hits a puck so that it comes to rest in $10 \mathrm{~s}$ after sliding $100 \mathrm{ft}$ on the ice. Determine $(a)$ the initial velocity of the puck, (b) the coefficient of friction between the puck and the ice.

Find the acceleration of an 800-kg car that has a net force of 4,000 N acting upon it.

A spring scale $A$ and a lever scale $B$ having equal lever arms are fastened to the roof of an elevator, and identical packages are attached to the scales as shown. Knowing that when the elevator moves downward with an acceleration of $1 \mathrm{~m} / \mathrm{s}^2$ the spring scale indicates a load of $60 \mathrm{~N}$, determine $(a)$ the weight of the packages, $(b)$ the load indicated by the spring scale and the mass needed to balance the lever scale when the elevator moves upward with an acceleration of $1 \mathrm{~m} / \mathrm{s}^2$.

A ball A is thrown vertically upward from the top of a 30-m-high building with an initial velocity of 5 m/s. At the same instant another ball B is thrown upward from the ground with an initial velocity of 20 m/s. Determine the height from the ground and the time at which they pass.

A certain drawbridge can be modeled as a uniform $15,000 \mathrm{~N}$ bar, $12.0 \mathrm{~m}$ long, pivoted about its lower end. When this bridge is raised to an angle of $60.0^{\circ}$ above the horizontal, the cable holding it suddenly breaks, allowing the bridge to fall. The instant after the cable breaks,
(a) what is the torque on this bridge about the pivot, and
(b) at what rate is its angular momentum changing?

A solid uniform cylinder with mass $8.25 \mathrm{~kg}$ and diameter $15.0 \mathrm{~cm}$ is spinning at $220 \mathrm{~rpm}$ on a thin, frictionless axle that passes along the cylinder axis. You design a simple friction brake to stop the cylinder by pressing the brake against the outer rim with a normal force. The coefficient of kinetic friction between the brake and rim is $0.333$. What must the applied normal force be to bring the cylinder to rest after it has turned through $5.25$ revolutions?

Three forces are applied to a wheel of radius 0.350, as shown in the figure (Intro 1figure). One force is perpendicular to the rim, one is tangent to it, and the other one makes a 40.0 angle with the radius. Assume that $F_1=12.4~\text{N}$, $F_2=14.2~\text{N}$, and $F_3=8.75~\text{N}$.

Part A What is the magnitude of the net torque on the wheel due to these three forces for an axis perpendicular to the wheel and passing through its center?

Part B What is the direction of the net torque in part (A), into the page or out of the page?

The 60-kg crate is sliding down the inclined plane. The coefficient of kinetic friction between the crate and the plane is 0.2, and the force P applied to the crate is constant. If the speed of the crate changes from 8 m/s to zero in 3 seconds, determine P.

The crate has a mass of $80 \mathrm{~kg}$ and is being towed by a chain which is always directed at $20^{\circ}$ from the horizontal as shown. Determine the crate's acceleration in $t=2 \mathrm{~s}$ if the coefficient of static friction is $\mu_s=0.4$, the coefficient of kinetic friction is $\mu_k=0.3$, and the towing force is $P=\left(90 t^2\right) \mathrm{N}$, where $t$ is in seconds.

The crate has a mass of $80 \mathrm{~kg}$ and is being towed by a chain which is always directed at $20^{\circ}$ from the horizontal. If the magnitude of $\mathbf{P}$ is increased until the crate begins to slide, determine the crate's initial acceleration if the coefficient of static friction is $\mu_s=0.5$ and the coefficient of kinetic friction is $\mu_k=0.3$.

A wheel rotates with a constant angular velocity of $6.00 \mathrm{rad} / \mathrm{s}$. a) Compute the radial acceleration of a point $0.500 \mathrm{~m}$ from the axis, using the relation $a_{\text {tad }}=\omega^2 r$. b) Find the tangential speed of the point and compute its radial acceleration from the relation $a_{\mathrm{rad}}=\frac{v^2}{ r}$