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.

Given that a frictionless plane is $10.0 \mathrm{~m}$ long and inclined at $35.0^{\circ}. \mathrm{A}$ sled starts at the bottom with an initial speed of $5.00 \mathrm{~m} / \mathrm{s}$ up the incline. When it reaches the point at which it momentarily stops, a second sled is released from the top of this incline with an initial speed $v_i$. Both sleds reach the bottom of the incline at the same moment. Calculate the distance that the first sled traveled up the incline.

A $60.0-\textrm{ kg}$ crate rests on a level floor at a shipping dock. The coefficients of static and kinetic friction are $0.760$ and $0.410$, respectively.

What horizontal pushing force is required to:

(a) just start the crate moving and

(b) slide the crate across the dock at a constant speed?

How long will it take for the crate to reach the floor if the height of the loading dock is $1.4 \mathrm{~m}$ above the floor?

A ball with a mass of 0.05 kg hits a frictionless, rigid, horizontal surface with the speed $v_1=20$ m / s at the angle $\theta_1=45^{\circ}$. The impulse acting on the ball during its contact with the surface is $1.8 N \cdot$ s. Find the rebound speed $v_2$ and the corresponding angle $\theta_2$.

A 60-kg crate is lowered from a loading dock to the floor using a rope passing over a fixed support. The rope exerts a constant upward force on the crate of 500 N.

What are the magnitude and direction of the acceleration of the crate?

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 boy having a weight of $80 \mathrm{lb}$ hangs uniformly from the bar. Determine the force in each of his arms in $t=2 \mathrm{~s}$ if the bar is moving upward with (a) a constant velocity of $3 \mathrm{ft} / \mathrm{s}$, and (b) a speed of $v=\left(4 t^2\right) \mathrm{ft} / \mathrm{s}$, where $t$ is in seconds.

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?

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?

A motorcycle travels along an unbanked curve of radius 200 m. If the static coefficient of friction between the road and the tires is 0.4, determine the largest constant speed at which the cycle will not slide.

One $3.0$-kg paint bucket is hanging by a massless cord from another $3.0$-kg paint bucket, also hanging by a massless cord, as shown in earlier Fig. (a) If the buckets are at rest, what is the tension in each cord? (b) If the two buckets are pulled upward with an acceleration of $1.60$ m/s$^2$ by the upper cord, calculate the tension in each cord.