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Chapter 6: Problem 88

In an adventure movie, a 62.5 -kg stunt woman falls \(8.10 \mathrm{m}\) and lands in a huge air bag. Her speed just before she hit the air bag was $10.5 \mathrm{m} / \mathrm{s} .$ (a) What is the total work done on the stunt woman during the fall? (b) How much work is done by gravity on the stunt woman? (c) How much work is done by air resistance on the stunt woman? (d) Estimate the magnitude of the average force of air resistance by assuming it is constant throughout the fall.

Short Answer

Expert verified
To find the total work done on the stunt woman during the fall, we will use the work-energy principle, and the given final speed of 10.5 m/s. Calculate the final kinetic energy using the formula: \(KE_f = \dfrac{1}{2} mv_f^2\) Subtract the initial kinetic energy (0, since the initial speed is 0) from the final kinetic energy: \(W_{total} = KE_f - KE_i\) Determine the total work done on the stunt woman during her fall.

Step by step solution

01

(Find the total work done on the stunt woman)

First, we will use the work-energy principle to find the total work done on the stunt woman during the fall. The work-energy principle states that the total work done on an object is equal to its change in kinetic energy: $$W_{total} = \Delta KE$$ We know her initial speed is 0 m/s (since she starts from rest), and her final speed is 10.5 m/s, as given in the problem. We can calculate her initial and final kinetic energies and find the difference: Initial kinetic energy \(KE_i = 0\) (because \(v_i = 0\)), Final kinetic energy \(KE_f = \dfrac{1}{2} mv_f^2\), $$W_{total} = KE_f - KE_i$$

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Most popular questions from this chapter

(a) How much work does a major-league pitcher do on the baseball when he throws a \(90.0 \mathrm{mi} / \mathrm{h}(40.2 \mathrm{m} / \mathrm{s})\) fastball? The mass of a baseball is 153 g. (b) How many fastballs would a pitcher have to throw to "burn off' a 1520 -Calorie meal? (1 Calorie \(=1000\) cal \(=1\) kcal.)Assume that \(80.0 \%\) of the chemical energy in the food is converted to thermal energy and only \(20.0 \%\) becomes the kinetic energy of the fastballs.
An ideal spring has a spring constant \(k=20.0 \mathrm{N} / \mathrm{m}\) What is the amount of work that must be done to stretch the spring \(0.40 \mathrm{m}\) from its relaxed length?
The escape speed from the surface of the Earth is $11.2 \mathrm{km} / \mathrm{s} .$ What would be the escape speed from another planet of the same density (mass per unit volume) as Earth but with a radius twice that of Earth?
A wind turbine converts some of the kinetic energy of the wind into electric energy. Suppose that the blades of a small wind turbine have length $L=4.0 \mathrm{m}$ (a) When a \(10 \mathrm{m} / \mathrm{s}(22 \mathrm{mi} / \mathrm{h})\) wind blows head-on, what volume of air (in \(\mathrm{m}^{3}\) ) passes through the circular area swept out by the blades in \(1.0 \mathrm{s} ?\) (b) What is the mass of this much air? Each cubic meter of air has a mass of 1.2 \(\mathrm{kg}\). (c) What is the translational kinetic energy of this mass of air? (d) If the turbine can convert \(40 \%\) of this kinetic energy into electric energy, what is its electric power output? (e) What happens to the power output if the wind speed decreases to \(\frac{1}{2}\) of its initial value? What can you conclude about electric power production by wind turbines?
Two springs with spring constants \(k_{1}\) and \(k_{2}\) are connected in series. (a) What is the effective spring constant of the combination? (b) If a hanging object attached to the combination is displaced by \(4.0 \mathrm{cm}\) from the relaxed position, what is the potential energy stored in the spring for \(k_{1}=5.0 \mathrm{N} / \mathrm{cm}\) and $k_{2}=3.0 \mathrm{N} / \mathrm{cm} ?$ [See Problem \(83(\mathrm{a}) .]\)
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