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Chapter 7: Q. 40 (page 179)

A $4.0 k g$ box is on a frictionless $35 掳$ slope and is connected via a massless string over a massless, frictionless pulley to a hanging $2.0 k g$ weight. The picture for this situation is similar to FIGURE P $7.39$ .
a. What is the tension in the string if the $4.0 k g$ box is held in place, so that it cannot move?
b. If the box is then released, which way will it move on the slope?
c. What is the tension in the string once the box begins to move?

Short Answer

Expert verified

(a) Tension in the spring if $4 k g$ box is held is $19.6 N$

(b) The moving direction o the box is anti-clockwise which is mass $m_{1}$ side.

(c) Tension in the spring, while the box is moving, is $20.56 N$

Step by step solution

01

Given information (part a)

$m_{1} = 4 k g$

$m_{2} = 2 k g$

$胃 = 35 掳$

02

Explanation (part a)

$F_{n e t} = m a F_{n e t} = m_{1} g \sin (胃) - m_{2} g m = m_{1} + m_{2} a = \frac{m_{1} g \sin (胃) - m_{2} g}{m_{1} + m_{2}} a = \frac{(4 k g) (9.8 m / s^{2}) (\sin (35 掳)) - (2 k g) (9.8 m / s^{2})}{4 k g + 2 k g} a = 0.48 m / s^{2}$

If the $4 k g$ box is held in place, then the tension will be because of only $2 k g$ box.

Tension T,

localid="1649649415107" $T = m_{2} g = (2 k g) (9.8 m / s^{2}) = 19.6 N$

03

Given information (part b)

$m_{1} = 4 k g$

$m_{2} = 2 k g$

$胃 = 35 掳$

04

Explanation (part b)

If the box is released direction will be in the anti-clock direction because a is coming positive and we assume the direction of an in anti clock wise direction.

05

Given information (part c)

$m_{1} = 4 k g$

$m_{2} = 2 k g$

$胃 = 35 掳$

06

Explanation (part c)

Tension in the string while box is moving

$F_{n e t} = m a T_{2} - m_{2} g = m_{2} a T_{2} = m_{2} g + m_{2} a a = 0.48 m / s^{2} m_{2} = 2 k g T_{2} = (2 k g) (9.8 m / s^{2}) + (2 k g) (0.48 m / s^{2}) = 20.56 N$

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Most popular questions from this chapter

Block $A$ in $F I G U R E E X 7.4$ is heavier than block $B$ and is sliding down the incline. All surfaces have friction. The rope is massless, and the massless pulley turns on frictionless bearings. The rope and the pulley are among the interacting objects, but you鈥檒l have to decide if they鈥檙e part of the system.

A woman living in a third-story apartment is moving out. Rather than carrying everything down the stairs, she decides to pack her belongings into crates, attach a frictionless pulley to her balcony railing, and lower the crates by rope. How hard must she pull on the horizontal end of the rope to lower a $25 k g$ crate at steady speed?

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