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Chapter 1: 45P (page 1)

A 100 kgblock is pulled at a constant speed of 5.0 m/sacross a horizontal floor by an applied force of 122 Ndirected $37^{掳}$ above the horizontal. What is the rate at which the force does work on the block?

Short Answer

Expert verified

The rate of doing work on the block is, $4.9 脳 10^{2} W$ .

Step by step solution

01

Given

The mass of block is, $m = 100 kg$ .

The force applied on block is, $F = 122 N$ .

The velocity of block is, $v = 5.0 m / s$ .

The direction of force is, $胃 = 37^{掳}$ .

02

Concept

The rate at which the force does the work on the object is called as power due to the force. The work done on a particle by a constant force during its displacement is given as

$W = \overset{鈫�}{F} . \overset{鈫�}{d}$

Formula:

$W = \overset{鈫�}{F} . \overset{鈫�}{d} P_{avg} = \frac{W}{鈭� t}$

03

Calculate the work done

The power due to force is the rate at which force does the work on the object.

$\begin{array}{rcl} P_{avg} & = & \frac{W}{鈭� t} \\ = & \frac{Fd 肠辞蝉胃}{t} \\ P_{avg} & = & Fv 肠辞蝉胃 \end{array}$

(As $\frac{d}{t} = v$ ),

Substitute all the value in the above equation.

$\begin{array}{rcl} P_{avg} & = & 122 N 脳 5.0 m / s 脳 \cos 37 \\ = & 4.9 脳 10^{2} W \end{array}$

Thus, the rate at which the force does work on the block $4.9 脳 10^{2} W$ .

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