Is it possible to whirl a bucket of water fast enough in a vertical circle so the water won't fall out? If so, what is the minimum speed?

How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95 km/h?

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 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.

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 tension in the cord, for an angle $\theta=32^{\circ}$.

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).

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.

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.

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 $68\,\mathrm{kg}$ 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 ball having a mass of $1.00 \mathrm{~kg}$ is attached to a string $1.00 \mathrm{~m}$ long and is whirled in a vertical circle at a constant speed of $10.0 \mathrm{~m} / \mathrm{s}$. a) Determine the tension in the string when the ball is at the top of the circle. b) Determine the tension in the string when the ball is at the bottom of the circle. c) Consider the ball at some point other than the top or bottom. What can you say about the tension in the string at this point?

A 500 g ball swings in a vertical circle at the end of a 1.5-m-long string. When the ball is at the bottom of the circle, the tension in the string is 15 N. What is the speed of the ball at that point?

In Fig. 5-36 the coefficient of static friction between mass $m_{\mathrm{A}}$ and the table is $0.40$, whereas the coefficient of kinetic friction is 0.30. What value(s) of $m_{\mathrm{A}}$ will keep the system moving at constant speed? [Ignore masses of the cord and the (frictionless) pulley.]

In Fig. 5-36 the coefficient of static friction between mass $m_{\mathrm{A}}$ and the table is $0.40$, whereas the coefficient of kinetic friction is 0.30. What minimum value of $m_{\mathrm{A}}$ will keep the system from starting to move?