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HW_7_solution

# HW_7_solution - P1112 Fall 2008 Solution to Homework#7 1 A...

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P1112 Fall 2008 Solution to Homework #7 1. A small remote-control car with mass 1.60 kg moves at a constant speed of v= 12.0 m/s in a vertical circle inside a hollow metal cylinder that has a radius of 5.00 m. What is the magnitude of the normal force exerted on the car by the walls of the cylinder at a) the bottom of the vertical circle and b) at the top of the vertical circle? At the bottom, the free body diagram has W=mg going down, and normal force N from the track going up. N-W=N-mg=ma=mv 2 /r or N=m(v 2 /r+g)=1.60 kg (12.0 2 /5+9.8) m/s 2 =61.8 N At the top, both the weight and the normal force are pointing downward, so N+mg= mv 2 /r N=m(v 2 /r-g)=30.4 N 2. The International Space Station (ISS) orbits the Earth in an approximately circular orbit at a height of about 240 miles (384 km) above the Earth's surface. (a) What is the speed of the space station in its orbit (in km/s)? Newton’s law of gravitation combined with the formula for centripetal acceleration gives GMm/r 2 =mv 2 /r so v= (GM/r)=7.7 km/s where r is the radius of the earth plus 384 km. (b) What is the space station's orbital period (in hours)? Period is circumference divided by velocity T=2 π r/v=1.5 hours 3. A neutral buoyancy torpedo of mass M=100kg is fired horizontally from one submarine to another. [Neutral buoyancy means that the buoyancy force exactly cancels the force of gravity.] The propellers on the torpedo provide a constant force of F=500N. Before reaching its target the torpedo reaches its terminal speed v t =30m/s. (a) When the torpedo reaches its terminal speed, what is the magnitude of the drag force?

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HW_7_solution - P1112 Fall 2008 Solution to Homework#7 1 A...

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