Question

1. A 40-kg person is riding on a Ferris wheel of radius 20-m. The wheel is moving with a speed of 6 m/s. Find the centripetal acceleration of the person on the ride. 2. Find the apparent weight (normal force) of the person in the previous question at a) the bottom of the wheel; b) the top of the wheel. 3. Suppose two stars orbit each other, each of the same mass as the Sun (2.0x10^30 kg). a) Find the gravitational force between the two stars if they are 3.0x10^12m apart.

Answer 1

m=40kg

r= 20 m

v= 6m/s

1. centripetal acceleration = v²/r =36/20 = 1.8 m/s²

2. At bottom, net force acting = mg + mv²/r = 40 x 9.8 + 40 x 1.8 = 464 N

At top, net force acting = mg - mv²/r = 40 x 9.8 - 40 x 1.8 = 320 N

3. m1 = m2 =m = 2 x 10³⁰ kg

r= 3 x 10¹² m

F= Gmm/r²

= (6.67 x 10^-11 ) ( 2 x 10³⁰) ( 2 x 10³⁰)/(3 x 10¹²)²

= 1.48 x 10^-5 N