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Chapter 7: Q.55 (page 180)

What is the acceleration of the $3.0 k g$ block in $F I G U R E C P 7.55$ across the frictionless table?
Hint: Think carefully about the acceleration constraint.

Short Answer

Expert verified

The acceleration of the $3.0 k g$ block is $2.8 m / s^{2}$

Step by step solution

01

Given information

mass of block $m_{1} = 3.0 k g$

mass of block $m_{2} = 1.0 k g$

All surfaces are frictionless.

02

Explanation

Consider the Forces of two masses given in the $f i g u r e C P 7.55$

For block mass $m_{1}$

$T_{1} = m_{1} a_{1}$

For block mass $m_{2}$

$m_{2} g - T_{2} = m_{2} a_{2}$

Considering the pulley is massless, $鈭� T_{1} = T_{2}$

Let $a_{2} = a$ $鈭� T = 2 m_{1} a$

$鈭� a_{1} = 2 a$ acceleration constraint

On substituting the above equations on block mass $m_{2}$ equation, we get

$m_{2} g - 2 m_{1} a = m_{2} a (2 m_{1} + m_{2}) a = m_{2} g a = \frac{m_{2} g}{(2 m_{1} + m_{2})}$

Therefore, the acceleration for $m_{1}$ is given by,

localid="1649865147826" $a_{1} = \frac{2 m_{2} g}{(2 m_{1} + m_{2})} = \frac{2 (1.0) (9.81)}{(2 (3.0) + 1.0)} = 2.8 m / s^{2}$

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Most popular questions from this chapter

The $10.2 k g$ block in FIGURE $P 7.37$ is held in place by a force applied to a rope passing over two massless, frictionless pulleys. Find the tensions $T_{1} t o T_{5}$ and the magnitude of force $\overset{鈫�}{F}$ .

The cable cars in San Francisco are pulled along their tracks by an underground steel cable that moves along at $9.5 m p h .$ The cable is driven by large motors at a central power station and extends, via an intricate pulley arrangement, for several miles beneath the city streets. The length of a cable stretches by up to $100 f t$ during its lifetime. To keep the tension constant, the cable passes around a $1.5 m$ diameter 鈥渢ensioning pulley鈥� that rolls back and forth on rails, as shown inFIGURE $100 f t$ . A $2000 k g$ block is attached to the tensioning pulley鈥檚 cart, via a rope and pulley, and is suspended in a deep hole. What is the tension in the cable car鈥檚 cable?

The hand in the figure is pushing on the back of block A. Blocks A and B, with $m_{b} > m_{a}$ are connected by a massless string and slide on a frictionless surface. Is the force of the string on B larger than, smaller than, or equal to the force of the hand on A? Explain.

Blocks with masses of $1 k g, 2 k g and 3 k g$ are lined up in a row on a frictionless table. All three are pushed forward by a $12 N$ force applied to the $1 k g$ block.

a. How much force does the $2 k g$ block exert on the $3 k g$ block?

b. How much force does the $2 k g$ block exert on the $1 k g$ block?

Blocks A and B in the figure are connected by a massless string over a massless, frictionless pulley. The blocks have just been released from rest. Will the pulley rotate clockwise, counterclockwise, or not at all? Explain.

See all solutions

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