Problem 1. A car moves at across a bridge made in the shape of a circular arc of radius \( r \). At what minimum speed will the normal force become zero if \( \mathrm{r}=25 \mathrm{~m} \) ? ( 5 pts.)
Problem 2. A rotating wheel requires 5 seconds to rotate 45 revolutions. Its angular velocity at the end of the 3 sec interval is \( 110 \mathrm{rad} / \mathrm{s} \). What is the constant angular acceleration of the wheel? ( 5 pts.)
Problem 3. A horse velocity increases at the constant rate of \( 0.77 \frac{\mathrm{~m}}{\mathrm{~s}^{2}} \) on a circular path with a radius of 1500 ft . Determine the velocity of the horse in which the magnitude of the centripetal is equal to the and tangential acceleration. ( 10 pts.)
Problem 4. Junjun has a 3.75 kg . ball and a rope, he attached the ball on the end of the rope and he started to swing. The ball moves in a circle of radius 0.75 m at an angular velocity of \( 0.75 \mathrm{rev} / \mathrm{sec} \). The tangential velocity and centripetal acceleration of the ball is? And if the maximum tension the rope can withstand before breaking is 125 N , what is the maximum tangential velocity the ball can have? ( 10 pts.)
Problem 5: Objects with masses of 350 lbs . and 750 lbs . are separated by 0.8 m . Find the net gravitational force exerted by these objects on a 155 lbs . object placed midway between them. At what position can the 155 lbs . object be placed so as to experience a net force of zero? (10 pts.)
