i cant get these problems !Relative to the ground, what is the gravitational potential energy of a 69.0-kg person who is at the top of the Sears Tower, a height of 443 m above the ground?A 0.050-kg arrow is fired horizontallyThe bowstring exerts an average force of 50 N on the arrow over a distance of 0.90 mWith what speed does the arrow leave the bow?A person is making homemade ice creamShe exerts a force of magnitude 22 N on the free end of the crank handle, and this end moves in a circular path of radius 0.25 mThe force is always applied parallel to the motion of the handleIf the handle is turned once every 1.1 s, what is the average power being expended?A 2.40 102-kg piano is being lifted at a steady speed from ground level straight up to an apartment 12.0 m above the groundThe crane that is doing the lifting produces a steady power of 4.00 102 WHow much time does it take to lift the piano?thank you so much !physics is really hardd :(
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Q1Gravitational potential energy mass x acceleration due to gravity x height 69 x 9.8 x 443 approx3.0 x 10^5 Joules Q2The work done on the arrow force x distance 50 N x 0.90 m 45 J The kinetic energy of the arrow equals the work done on itKinetic energy (1/2) x mass x (velocity^2) So (1/2) x mass x (velocity^2) 45 J mass x (velocity^2) 90 J So the arrow leaves the bow with a velocity (speed) of sqrt (90 / 0.050) sqrt (1800) approx42 m/s Q3The radius 0.25 m so the circumference 2 pi r approx1.57 m The handle is turned once every 1.1 seconds, so its speed is (1.57/1.1) m/s 1.43 m/s (approx.) The average power being expended force x speed 22 N x 1.43 m/s 31.4 W Q4I puzzled over this one, since I'm pretty sure pianos weigh a lot more than 102 kgI think you meant to write 2.40 x 10^2 kg (i.e240 kg)Similarly, the power is 4.00 x 10^2 W (i.e400 W)The weight of the piano (the downward force it exerts) 240 x 9.8 2352 N The crane must exert an equal and opposite force on the pianopower force x speed force x (distance/time) So the time taken force x distance / power 2352 x 12 / 400 approx70 seconds
