Ch6_2
 
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Make sure to calculate your answers in SI units unless specified otherwise .
1) A kg object slides on a horizontal plane and is stopped by friction after a distance of m. What is the initial kinetic energy when the coefficient of friction of the object-plane interface is (see sheet 15,19,19') ? Indicate with a negative (positive) sign whether the object changes (does not change) its potential energy during the slide.
2) A block, starting at rest and from a height of m, slides down a frictionless inclined plane. At the bottom the block continues to slide horizontally and is brought to a halt after m by friction. What is the coefficient of friction of the block-horizontal-plane interface (see sheet 15,17,18-19') ? Indicate with a negative (positive) sign whether the block changes both its kinetic and potential (only its kinetic) energy during the slide on the inclined plane.
3) A 50 kg person starting with an initial downward velocity of m/s dips into a m deep pool. If J kinetic energy are lost due to friction what is the arrival speed at the bottom of the pool (see sheet 15) (If you know about "Buoyancy" disregard it) ? Indicate with a negative (positive) sign whether the potential energy of the person does (does not) change while sinking in the pool.
NOTE! For #4,5,6 use the numbers given in the lecture notes for the radius and the mass of the earth.

 4) A kg object is lifted from the surface of the earth to a height of km above the surface of the earth. Calculate the increase in gravitational potential energy using the exact expression (see sheet 24) and compare it with the approximate expression using g=9.81 (see sheet 12,24'). Give the magnitude of the difference between the two expressions divided by the exact result (that is the relative error) as your answer. Make sure you use at least 6 significant digits when calculating the difference. Indicate with a positive (negative) sign whether your relative error is less than (greater than) a 1% accuracy .

5) A kg piece of a satellite left over from an explosion with zero orbital velocity in space falls from a distance of km above the surface of the earth down toward earth. It arrives with MJ (M="mega") kinetic energy on earth. How many MJ energy have been lost due to friction in the earth's atmosphere ? Use the exact expression (see sheet 24) for the gravitational potential energy. Make sure you use at least 6 significant digits when calculating the change in potential energy. Indicate with a negative (positive) sign whether the kinetic energy at arrival would be larger (smaller) than the MJ without friction in the atmosphere.
6) Calculate the escape velocity for a planet with the moon's mass (7.4x1022 kg) and a mean radius of x106 m (see sheet 26,27) ? Indicate with a positive (negative) sign whether the value for the earth is larger (smaller) than your result.

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