Question

1) A coin is placed on a large disk which rotates uniformly at a rate of 2 rot/s. The coefficient of friction between the coin and the disk is 0.1. To what distance from the center of the disk should the coin be placed so that the coin may not slip?

2) A 1663 -kg car moves on a horizontal curved road. If the radius of the curve is 42 m and the coefficient of friction between the tires and road is 0.1, find the maximum speed the car can have so that it may not skid.

3) A small sphere of mass 2 kg is attached to the end of a cord of length 3m and rotated in a vertical circle about a fixed point O. Determine the tension in the cord at the uppermost point of the trajectory if the speed at this point is 8m/s. Use g=9.8 m/s².

4) A small sphere of mass 2 kg is attached to the end of a cord of length 2m and rotated in a vertical circle about a fixed point O. Determine the tension in the cord at the lowest point of the trajectory if the speed at this point is 9m/s. Use g=9.8 m/s².

5) True or False? A small sphere of mass 1 kg is attached to the end of a cord of length 1 m and rotated in a vertical circle about a fixed point O. If the speed at the uppermost point of the trajectory is 1 m/s, the sphere will have a circular trajectory (will move in a circle).
Use g=9.8 m/s².

Answer 1

1) so we need u m g = m w^2 r

u g = w^2 r

r = u g/w^2 = 0.1*9.81/(2*2*pi)^2=0.00621 m

2) um g = mv^2/r

v = sqrt( u g r) = sqrt(0.1*9.81*42)= 6.42 m/s

3) at top

T + m g = mv^2/r

T = mv^2/r - mg = 2*(8^2/3-9.81)=23.05 N

4) at lowest point

T - mg = mv^2/r

T = mg + mv^2/r = 2*(9^2/2+9.81)=100.62 N

5)

so if moving in a circle T + m g = mv^2/r

so smallest T is when T = 0

mg = 1*9.8 = 9.8

mv^2/r = 1*1^2/1 = 1

T = mv^2/r - mg = 1-9.8 = -8.8

can't have negative T so doesnt move in a circle
so False