is a bird’s-eye view of particles on strings moving in horizontal circles on a tabletop. All are moving at the same speed. Rank in order, from largest to smallest, the tensions . Give your answer in the formand explain your ranking.
The tensions are ranked in the order:
The tensions at mass with velocity and radiusof circular motion
Centripetal force equal to tension acting on the string.
The free-body diagram shows that the downward gravitational force is balanced by an upward component of the tension, leaving the radial component of the tension to cause the centripetal acceleration. Newton’s second law is
The above tension equation is applied for the given cases of free body diagram of FIGURE Q8.3
case (a): The tension at mass m with velocity v and radius of circular motion gives
case (b): The tension at mass m with velocity v and radius of circular motion gives
case (c): The tension at mass m with velocity v and radius of circular motion gives
case (d): The tension at mass m with velocity v and radius of circular motion gives
The Tensions of each string for different cases are ranked in the order
While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be , and you use your watch to find that each loop around takes .
a. What are your speed and the magnitude of your acceleration?
b. What is the ratio of your weight at the top of the ride to your weight while standing on the ground?
c. What is the ratio of your weight at the bottom of the ride to your weight while standing on the ground?
A model rocket is resting horizontally at the top edge of a -high wall when it is accidentally bumped. The bump pushes it off the edge with a horizontal speed of m/s and at the same time causes the engine to ignite. When the engine fires, it exerts a constant horizontal thrust away from the wall.
a. How far from the base of the wall does the rocket land?
b. Describe the rocket’s trajectory as it travels to the ground
A motorcycle daredevil plans to ride up a -high, ramp, sail across a -wide pool filled with hungry crocodiles, and land at ground level on the other side. He has done this stunt many times and approaches it with confidence. Unfortunately, the motorcycle engine dies just as he starts up the ramp. He is going at that instant, and the rolling friction of his rubber tires (coefficient ) is not negligible. Does he survive, or does he become crocodile food? Justify your answer by calculating the distance he travels through the air after leaving the end of the ramp.
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