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Chapter 6: Problem 1

How much work must Denise do to drag her basket of laundry of mass $5.0 \mathrm{kg}\( a distance of \)5.0 \mathrm{m}$ along a floor, if the force she exerts is a constant \(30.0 \mathrm{N}\) at an angle of \(60.0^{\circ}\) with the horizontal?

Short Answer

Expert verified
Answer: Denise does 75.0 Joules of work to drag her laundry basket the required distance.

Step by step solution

01

Identify the given values and the formula for work

We are given the mass of the laundry basket (m = 5.0 kg), the distance it is dragged (d = 5.0 m), the force exerted by Denise (F = 30.0 N), and the angle between the force and horizontal direction (θ = 60.0°). The formula for work is: Work = Force × Distance × cos(θ)
02

Convert the angle to radians

We need to convert the angle from degrees to radians before calculating the work. θ (in radians) = (60.0 * π) / 180 = π / 3
03

Calculate the horizontal component of the force

We now determine the horizontal component of the force (F_horizontal) by multiplying the force by the cosine of the angle: F_horizontal = F × cos(θ) = 30.0 N × cos(π / 3) = 30.0 N × 0.5 = 15.0 N
04

Calculate the work done

Finally, we calculate the work performed by Denise by multiplying the horizontal component of the force by the distance the laundry basket is dragged: Work = F_horizontal × d = 15.0 N × 5.0 m = 75.0 J Denise must do 75.0 Joules of work to drag her basket of laundry 5.0 meters along the floor.

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