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Chapter 5: Problem 52

How much work is done against gravity in lifting a \(6.00-\mathrm{kg}\) weight through a distance of \(20.0 \mathrm{~cm} ?\)

Short Answer

Expert verified
Answer: The work done against gravity is 11.772 J.

Step by step solution

01

Convert distance

First, we need to convert the given distance from centimeters to meters, since we'll be working in SI units. To do this, remember that there are \(100\) centimeters in a meter: \(20.0\mathrm{~cm} = 20.0/100\mathrm{~m} = 0.200\mathrm{~m}\).
02

Calculate gravitational force

Next, we need to find the gravitational force acting on the weight. This is given by the formula \(F = m \times g\), where \(m\) is the mass of the weight and \(g\) is the gravitational acceleration (\(9.81\mathrm{~m/s^2}\)). So the gravitational force is: \(F = 6.00\mathrm{~kg} \times 9.81\mathrm{~m/s^2} = 58.86\mathrm{~N}\).
03

Compute work done against gravity

Now that we have the distance and the gravitational force, we can calculate the work done against gravity using the formula for work: \(W = F \times d \times \cos{\theta}\). Since the angle is \(0^{\circ}\), the cosine of the angle is \(1\). Therefore, the work done against gravity is: \(W = 58.86\mathrm{~N} \times 0.200\mathrm{~m} \times 1 = 11.772 \mathrm{~J}\) (joules). So, the work done against gravity in lifting the \(6.00-\mathrm{kg}\) weight through a distance of \(20.0\mathrm{~cm}\) is \(11.772\mathrm{~J}\).

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Most popular questions from this chapter

How much work do movers do (horizontally) in pushing a \(150-\mathrm{kg}\) crate \(12.3 \mathrm{~m}\) across a floor at constant speed if the coefficient of friction is \(0.70 ?\) a) 1300 J c) \(1.3 \cdot 10^{4}\) ] e) 130 ] b) 1845 J d) \(1.8 \cdot 10^{4}\) ]

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