1.) On a hot summer day, a young girl swings on a rope above the local swimming hole. When she lets go of the rope her initial velocity is 2.25m/s at and angle of 35.0 degrees above the horizontal. If she is in flight for 0.616s, how high above the water was she when she let go of the rope?
2.) A wooden block of 20.0 kg rests on a horizontal wooden plank. The plank is lifted by one end until it forms a 40.0degree angle with the floor. The coefficient of kinetic friction between the surfaces is 0.20.
a. Does the block slide down the plank at this angle?
b.) At what minimum angle does the block start to slide?
c. Assume the plank is 12m long and that the block is at the top of the plank. What is the velocity of the block at the bottom when it slides all the way down this 40.0degree incline?
3. Consider an asteroid with a radius of 14km and a mass of 3.35 x 10^15kg. Assume the asteroid is roughly spherical.
a. What is the acceleration due to gravity on the surface of the asteroid?
b. Suppose the asteroid spins about an axis through its center, like the Earth, with rotational period T. What is the smallest value T can have before loose rocks on the asteroid’s equator begin to fly off the surface?
4. An engineer is designing a carousel for an amusement park. The ride will be 15m in diameter and when filled with riders will weigh 25,000kg, all balanced and rotating about a central axis.
a. Calculate the carousel’s moment of inertia. Assume the ride behaves like a solid cylinder.
b. The carousel may also be designed with 12 uniformly spaced rods fixed like the spokes of a wheel around a center of rotation. Assuming the outward weight and dimensions are the same, is the moment of inertia for this rod design greater than or less than the design used in part a?
c. For an entertaining attraction, the carousel should not move the riders at the outer edge of the carousel (given in part a) faster than 3.0m/s. Calculate the maximum angular velocity of the carousel.
d. For maximum enjoyment, the carousel in part (a) should reach maximum angular velocity within 30 seconds of starting from rest. Calculate the minimum angular acceleration that would accomplish this velocity.
e. Calculate the net torque necessary for this carousel so a motor can be purchased. (use the design in part A for ur calculations)
5. Two balls have the same diameter. The less massive ball (m=0.15kg) is placed on top of the more massive ball(m=0.85kg). The balls are dropped from rest onto a concrete floor. Before release, the bottom of the lower ball is 15.0m above the floor, ad the balls remain in contact until they hit the floor.
a. In a first trial, the 0.85kg ball remains stationary after impact with the ground. Using the law of conservation energy, calculate the speed of the 0.15kg ball just after impact. Assume the collision is perfectly elastic.
b. What is the maximum height the 0.15kg ball can reach after impact?
c. In a second trial, the balls are released from the same height, but the 0.85kg ball is now on top of the 0.15 kg ball. What is the maximum height of the 0.85kg ball after impact? What will be the ball’s velocity when it reaches its maximum height?
d. In a third trial, two balls with equal mass (0.15kg) are released from the same starting position. This time, both ball rebound after impact at a 45degree angle to the vertical. What will be the maximum height of each ball? What will be the balls’ velocities when they reach their maximum height?
I did not ask for any smart comments like the ones Paschal H wrote. If you have a smart alick opinion just dont answer the question
