Two masses $m_{\mathrm{A}}=2.0 \mathrm{~kg}$ and $m_{\mathrm{B}}=5.0 \mathrm{~kg}$ are on inclines and are connected together by a string as shown in Fig. $5-38$. The coefficient of kinetic friction between each mass and its incline is $\mu_{\mathrm{k}}=0.30$. If $m_{\mathrm{A}}$ moves up, and $m_{\mathrm{B}}$ moves down, determine their acceleration. Ignore the masses of the cord and the pulley (assume frictionless).

A puck of mass $m=1.50 \mathrm{~kg}$ slides in a circle of radius $r=20.0 \mathrm{~cm}$ on a frictionless table while attached to a hanging cylinder of mass $M=2.50 \mathrm{~kg}$ by means of a cord that extends through a hole in the table. What speed keeps the cylinder at rest?

Two masses mA = 2.0 kg and mB = 5.0 kg are on inclines and are connected together by a string as shown in the figure. The coefficient of kinetic friction between each mass and its incline is muk = 0.30. If mA moves up, and mB moves down, determine the magnitude and direction of the acceleration.

A $75-\mathrm{~kg}$ snowboarder has an initial velocity of $5.0 \mathrm{~m} / \mathrm{~s}$ at the top of a $28^{\circ}$ incline (Fig. 5-36). After sliding down the 110-m long incline (on which the coefficient of kinetic friction is $\mu_{\mathrm{~k}}=0.18$ ), the snowboarder has attained a velocity $v$. The snowboarder then slides along a flat surface (on which $\mu_{\mathrm{~k}}=0.15$ ) and comes to rest after a distance $x$. Use Newton's second law to determine the snowboarder's acceleration while on the incline and while on the flat surface. Then use these accelerations to determine $x$.

A puck of mass m=1.50 kg slides in a circle of radius r=20.0 cm on a frictionless table while attached to a hanging cylinder of mass $M=2.50 \mathrm{~kg}$ by a cord through a hole at the center in the table. What speed keeps the cylinder at rest?

Two blocks of mass $3.50\mathrm{~kg}$ and $8.00\mathrm{~kg}$ are connected by a massless string that passes over a frictionless pulley and rests on inclines who makes $35.0^{\circ}$ with the horizontal. The inclines are frictionless. Find
(a)the magnitude of the acceleration of each block.
(b) the tension in the string.

Two blocks made of different materials connected together by a thin cord slide down a ramp inclined at an angle $\theta$ to the horizontal, Fig. 5-40 (block B is above block A). The masses of the blocks are $m_{\mathrm{A}}$ and $m_{\mathrm{B}}$, and the coefficients of friction are $\mu_{\mathrm{A}}$ and $\mu_{\mathrm{B}}$. If $m_{\mathrm{A}}=m_{\mathrm{B}}=4.0 \mathrm{~kg}$, and $\mu_{\mathrm{A}}=0.20$ and $\mu_{\mathrm{B}}=0.30$, find the acceleration of the blocks.

Highway curves are marked with a suggested speed. Find the maximum speed for a flat road for which the curve has a radius $r$ and static friction coefficient $\mu$

Highway curves are marked with a suggested speed. If this speed is based on what would be safe in wet weather, estimate the radius of curvature for an unbanked curve marked $50 \mathrm{~km} / \mathrm{h}$. Use Table $5-1$ (coefficient of friction).

A $68\,\mathrm{kg}$ snowboarder has an initial velocity of $5.0 \mathrm{~m} / \mathrm{s}$ at the top of a $28^{\circ}$ incline (Fig. 5-37). After sliding down the $110\,\mathrm{m}$ long incline (assume a coefficient of kinetic friction $\mu_{\mathrm{k}}=0.18$ ), the snowboarder has attained a velocity $v$. The snowboarder then slides along a flat surface (on which $\mu_{\mathrm{k}}=0.15$ ) and comes to rest after a distance $x$. Use Newton's second law to find the snowboarder's acceleration while on the incline and while on a flat surface. Then use these accelerations to determine $x$. Ignore air resistance.

A grocery cart with mass of $16 \mathrm{~kg}$ is being pushed at constant speed up a flat $12^{\circ}$ ramp by a force $F_{\mathrm{~P}}$ which acts at an angle of $17^{\circ}$ below the horizontal. Determine the work done by each of the forces $\left(m \overrightarrow{\mathbf{g}}, \overrightarrow{\mathbf{~F}}_{\mathrm{N}}, \overrightarrow{\mathbf{F}}_{\mathrm{P}}\right)$ on the cart if the ramp is $15 \mathrm{~m}$ long.

A grocery cart with mass of $18$ kg is pushed at constant speed along an aisle by a force $F=12 \mathrm{~N}$. The applied force acts at a $20\degree$ angle to the horizontal. Find the work done by each of the forces on the cart if the aisle is $15$ m long.

Two blocks made of different materials connected together by a thin cord, slide down a plane ramp inclined at an angle $\theta$ to the horizontal as shown in Fig. 5-34 (block B is above block A). The masses of the blocks are $m_{\mathrm{A}}$ and $m_{\mathrm{B}}$, and the coefficients of friction are $\mu_{\mathrm{A}}$ and $\mu_{\mathrm{B}}$. If $m_{\mathrm{A}}=m_{\mathrm{B}}=5.0 \mathrm{~kg}$, and $\mu_{\mathrm{A}}=0.20$ and $\mu_{\mathrm{B}}=0.30$, Find the acceleration of the blocks.

Two blocks made of different materials connected together by a thin cord, slide down a plane ramp inclined at an angle $\theta$ to the horizontal as shown in Fig. 5-34 (block B is above block A). The masses of the blocks are $m_{\mathrm{A}}$ and $m_{\mathrm{B}}$, and the coefficients of friction are $\mu_{\mathrm{A}}$ and $\mu_{\mathrm{B}}$. If $m_{\mathrm{A}}=m_{\mathrm{B}}=5.0 \mathrm{~kg}$, and $\mu_{\mathrm{A}}=0.20$ and $\mu_{\mathrm{B}}=0.30$, Find the tension in the cord, for an angle $\theta=32^{\circ}$.