I was looking over some old practice tests supplied by my professorand I am havi

Question

I was looking over some old practice tests supplied by my professorand I am having some trouble on a couple problems. Any helpwould be greatly appreciated.

1) A 0.50-kg ob ject moves in a horizontal circular trackwith a radius of 2.5 m. An external force of 3.0 N, always tangentto the track, causes the ob ject to speed up as it goes around. Thework done by the external force as the mass makes one revolutionis:

2) A 25-g ball is released from rest 80 m above the surfaceof the Earth. During the fall the total thermal energy of the balland air increases by15 J. Just before it hits the surface its speedis


Thanks a lot!

Explanation / Answer

(1). mass m = 0.5 kg radius r = 2.5 m Circumference S = 2r = 15.7 m external force F = 3 N work done W = F S                       = 47.12 J (2). mass m = 25 g  =0.025 kg Initial speed   u = 0 height h = 80 m    Increase in thermal energy of the ball and air E =15 J Potential energy at height h is E ' = mgh =19.6 J Kinetic energy of the ball when it hits the ground E " =E ' - E = 4.6 J we know E " = ( 1/ 2) m v ^ 2 from this required velocity v = [ 2E" / m ]                                            = 19.18 m / s

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