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Chapter 3: Problem 18
A \(523-\mathrm{kg}\) experimental rocket sled can be accelerated from rest to \(1620 \mathrm{~km} / \mathrm{h}\) in \(1.82 \mathrm{~s}\). What net force is required?
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(a) Neglecting gravitational forces, what force would be required to accelerate a 1200-metric-ton spaceship from rest to one-tenth the speed of light in 3 days? In 2 months? (One metric ton \(=1000 \mathrm{~kg} .)(b)\) Assuming that the engines are shut down when this speed is reached, what would be the time required to complete a 5-light-month journey for each of these two cases? (Use 1 month \(=30\) days.)
The Sun yacht Diana, designed to navigate in the solar system using the pressure of sunlight, has a sail area of \(3.1 \mathrm{~km}^{2}\) and a mass of \(930 \mathrm{~kg}\). Near Earth's orbit, the Sun could exert a radiation force of \(29 \mathrm{~N}\) on its sail. (a) What acceleration would such a force impart to the craft? (b) A small acceleration can produce large effects if it acts steadily for a long enough time. Starting from rest then, how far would the craft have moved after 1 day under these conditions? ( \(c\) ) What would then be its speed? (See "The Wind from the Sun," a fascinating science fiction account by Arthur C. Clarke of a Sun yacht race.)
A 77 -kg person is parachuting and experiencing a downward acceleration of \(2.5 \mathrm{~m} / \mathrm{s}^{2}\) shortly after opening the parachute. The mass of the parachute is \(5.2 \mathrm{~kg} .\) (a) Find the upward force exerted on the parachute by the air. (b) Calculate the downward force exerted by the person on the parachute.
An electron is projected horizontally at a speed of \(1.2 \times\) \(10^{7} \mathrm{~m} / \mathrm{s}\) into an electric field that exerts a constant vertical force of \(4.5 \times 10^{-16} \mathrm{~N}\) on it. The mass of the electron is \(9.11 \times 10^{-31} \mathrm{~kg} .\) Determine the vertical distance the electron is deflected during the time it has moved forward \(33 \mathrm{~mm}\) horizontally.
A man of mass \(83 \mathrm{~kg}\) (weight \(180 \mathrm{lb}\) ) jumps down to a concrete patio from a window ledge only \(0.48 \mathrm{~m}(=1.6 \mathrm{ft})\) above the ground. He neglects to bend his knees on landing, so that his motion is arrested in a distance of about \(2.2 \mathrm{~cm}(=0.87\) in.). ( \(a\) ) What is the average acceleration of the man from the time his feet first touch the patio to the time he is brought fully to rest? ( \(b\) ) With what average force does this jump jar his bone structure?
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