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Chapter 1: Q59P (page 1)

A force ${\overset{鈫�}{F}}_{a}$ is applied to a bead as the bead is moved along a straight wire through displacement $+ 5.0 c m$ . The magnitude ofrole="math" localid="1657167569087" ${\overset{鈫�}{F}}_{a}$ is set at a certain value, but the $蠒$ angle ${\overset{鈫�}{F}}_{a}$ between and the bead鈥檚 displacement can be chosen. Figure $7 - 45$ gives the work $W$ done byon the bead for a range of role="math" localid="1657166842505" $蠒$ values;role="math" localid="1657167794268" $W_{0} = 25 J$ . How much work is done byrole="math" localid="1657167547441" ${\overset{鈫�}{F}}_{a}$ if $蠒$ is (a) $64 掳$ and (b) $147 掳$ ?

Short Answer

Expert verified

Work done when $蠒 = 64 掳$ is $11 J$ .
Work done when $蠒 = 147 掳$ is $- 21 J$ .

Step by step solution

01

Given information

It is given that, graph of work done with various values of,

$W_{0} = 25 J, when 蠒 = 0, \begin{matrix} x = 5.0 cm \\ = 0.05 m \end{matrix} .$

02

Determining the concept

The problem deals with the power and the work done. Work, energy, and power are the fundamental concepts of physics. Work is the displacement of an object when force is applied on it.By using the value of $W_{0}$ find the applied force $F_{a}$ , which can be used to find the work done $64 掳$ cat and $147 掳$ .

Formula:

$W = F d \cos 蠁$

where,F is force, dis displacement and Wis the work done

03

(a) determining the work done when φ=64°

From the graph,

$W_{0} = 25 J W_{0} = F_{a} . x F_{a} = \frac{25}{0.05} F_{a} = 500 N$

Hence, work done when $蠒 = 64 掳$ is $11 J$ .

04

(b) determining the work done when ϕ=147°.

Work done when $蠒 = 64 掳$ ,

W = F_{a} 脳 \cos 64 W = 500 脳 0.05 脳 0.4383 W = 10.9575 J W 鈮� 11 J W = F_{a} 脳 \cos 147 W = 500 脳 0.05 脳 (- 0.8386) W = - 20.96 J W = - 20.96 J W 鈮� - 21 J

Hence, work done when $蠒 = 147 掳$ is $- 21 J$ .

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Most popular questions from this chapter

A ton is a measure of volume frequently used in shipping, but that use requires some care because there are at least three types of tons: A displacement ton is equal to 7 barrels bulk, a freight ton is equal to 8 barrels bulk, and a register ton is equal to 20 barrels bulk. A barrel bulk is another measure of volume: $1 barrel bulk = 0.1415 m^{3}$ . Suppose you spot a shipping order for 鈥�73 tons鈥� of $M & M$ candies, and you are certain that the client who sent the order intended 鈥渢on鈥� to refer to volume (instead of weight or mass, as discussed in Chapter 5). If the client actually meant displacement tons, how many extra U.S. bushels of the candies will you erroneously ship if you interpret the order as (a) 73 freight tons and (b) 73 register tons? ( $1 m^{3} = 28.378$ U.S. bushels.)

An astronomical unit (AU) is the average distance between Earth and the Sun, approximately $^{1.50 脳 10^{8} km}$ . The speed of light is about $^{3.0 脳 10^{8} m / s}$ . Express the speed of light in astronomical units per minute.

Suppose that, while lying on a beach near the equator watching the Sunset over a calm ocean, you start a stopwatch just as the top of the Sun disappears. You then stand, elevating your eyes by a height H = 1.70 m, and stop the watch when the top of the Sun again disappears. If the elapsed time is t = 11.1 s, what is the radius r of Earth?

Until 1883, every city and town in the United States kept its own local time. Today, travelers reset their watches only when the time change equals 1.0 h. How far, on the average, must you travel in degrees of longitude between the time-zone boundaries at which your watch must be reset by 1.0 h? (Hint: Earth rotates 360掳 in about 24 h.)

Water is poured into a container that has a small leak. The mass m of the water is given as a function of timetby $m = 5.00 t^{0.8} 鈥� 3.00 t + 20.00$ , with $t 鈮� 0$ ,min grams, andtin seconds. (a) At what time is the water mass greatest, and (b) what is that greatest mass? In kilograms per minute, what is the rate of mass change at (c) $t = 2.00 s$ and (d) $t = 5.00 s$ ?

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