A crate is given an initial speed of $3.0 \mathrm{~m} / \mathrm{s}$ up the $25.0^{\circ}$ plane shown in Fig. 5-35. How much time elapses before it returns to its starting point? Assume $\mu_{\mathrm{k}}=0.17$.

A child slides down a slide with a $28^{\circ}$ incline, and at the bottom, her speed is precisely half what it would have been if the slide had been frictionless. Determine the coefficient of kinetic friction between the slide and the child.

A child slides down a slide with a $28\degree$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

The crate shown in Fig. $5-33$ lies on a plane tilted at an angle $\theta=25.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{~k}}=0.19$. If the crate starts from rest $8.15 \mathrm{~m}$ up the plane from its base, what will be the crate's speed when it reaches the bottom of the incline?

A 27-kg chandelier hangs from a ceiling on a vertical 4.0-m-long wire.

a) What horizontal force would be necessary to displace its position 0.14 m to one side?

b) What will be the tension in the wire?

The crate shown in Fig. $5-35$ lies on a plane tilted at an angle $\theta=25.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.19$. If the crate starts from rest $8.75 \mathrm{~m}$ up the plane from its base, what will be the crate's speed when it reaches the bottom of the incline?

The crate shown in the figure lies on a plane tilted at an angle theta = 25.0 degrees to the horizontal, with mu_k = 0.19.

a. Determine the acceleration of the crate as it slides down the plane.

b. If the crate starts from rest 8.15 m up along the plane from its base, what will be the crate's speed when it reaches the bottom of the incline?

A car starts down a long slippery hill inclined at $15^{\circ}$. The brakes are applied at the top of the hill where the car's speed is $22.0 \mathrm{~m} / \mathrm{s}$. If the coefficient of static friction between the road and the tires is $0.35$ and the car slows at its maximum possible rate, how far will the car travel down the hill before stopping?

Two crates, of mass $65 \mathrm{~kg}$ and $125 \mathrm{~kg}$, are in contact and at rest on a horizontal surface (Fig. 5-34). A $650-\mathrm{N}$ force is exerted on the $65-\mathrm{kg}$ crate. If the coefficient of kinetic friction is $0.18$, estimate the force that each crate exerts on the other and the acceleration with the crates reversed.

A $27\,\text{kg}$ chandelier hangs from a ceiling on a vertical $4.0\,\text{m}$ long wire. What horizontal force would be necessary to displace its position $0.15 \mathrm{~m}$ to one side?

The crate shown in Fig. $5-35$ lies on a plane tilted at an angle $\theta=25.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.19$. Find the acceleration of the crate as it slides down the plane.

A wet bar of soap slides freely down a ramp $7.5 \mathrm{~m}$ long inclined at $8.0^{\circ}$. Starting from rest, how long does it take to reach the bottom? Assume $\mu_{\mathrm{k}}=0.060$.

A $27\,\text{kg}$ chandelier hangs from a ceiling on a vertical $4.0\,\text{m}$ long wire. What will be the tension in the wire?

A $27\,\mathrm{kg}$ chandelier hangs from a ceiling on a vertical $3.4\,\text{m}$ long wire. What will be the tension in the wire?