Question

Find a_c, F_c, and name the force responsible for the circular motion.

3.     The flying pig toy (mass of 1.2 x 10^-1 kg) suspended on a string makes one orbit at 2 m/s in 1.2 seconds.

4.     Flo- Joe (Mass of 59 kg) could round a 400 m track and 46.3 seconds.

5.     Mario Drive his car (Mass 715 kg) around the track at a speed of 2.43 x 10⁵ kilometers per hour in the 72.5 seconds.

Answer 1

3. mass m=0.12 kg

velocity v=2 m/s

distance=speed*time

here, speed=2 m/s , time=1.2 s

So,distance=2*1.2=2.4 m

If the radius of circular path is r, distance traveled in one orbit=2r

So, 2r=2.4=>r=0.382 m

So, centripetal acceleration a=v² / r =2*2/0.382=10.47 m/s²

Force=mass*acceleration=0.12*10.47=1.26 N

This force is provided by tension in string.

4.distance=400 m, time=46.3 seconds=>speed=distance/time=400/46.3=8.64 m/s

Also, distance traveled in one orbit=2r where r is radius.

So,2r=400=>r=63.66 m

So, centripetal acceleration =v²/r=8.64*8.64/63.66=1.17 m/s²

force=mass*acceleration=59*1.17=69.03 N

this force is provided by static friction.

5.speed=2.43*10⁵ km/h=2.43*10⁵*1000/3600=67500 m/s

time=72.5 s

distance=speed*time=67500*72.5=4893750 m

Also, distance traveled in one orbit=2r where r is radius.

So,2r=4893750 =>r=778864.5 m

So, centripetal acceleration =v²/r=67500*67500/778864.5=5849.86 m/s²

force=mass*acceleration=715*5849.86=4182649.9 N

Force responsible for this motion is static friction.