An athlete swings a 4.00-kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.740 m at an angular speed of 0.750 rev/s.(a)What is the tangential speed of the ball? m/s(b)What is its centripetal acceleration? m/s2(c)If the maximum tension the rope can withstand before breaking is 140 N, what is the maximum tangential speed the ball can have? m/s
Question
An athlete swings a 4.00-kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.740 m at an angular speed of 0.750 rev/s.(a)What is the tangential speed of the ball? m/s(b)What is its centripetal acceleration? m/s2(c)If the maximum tension the rope can withstand before breaking is 140 N, what is the maximum tangential speed the ball can have? m/s
Solution
(a) To find the tangential speed of the ball, we first need to convert the angular speed from revolutions per second to radians per second. We know that 1 revolution is equal to 2π radians. So, the angular speed in radians per second is 0.750 rev/s * 2π rad/rev = 1.5π rad/s.
The tangential speed (v) is given by the formula v = rω, where r is the radius and ω is the angular speed. Substituting the given values, we get v = 0.740 m * 1.5π rad/s = 3.51 m/s.
(b) The centripetal acceleration (a) is given by the formula a = v²/r. Substituting the values we have, we get a = (3.51 m/s)² / 0.740 m = 16.7 m/s².
(c) The maximum tension the rope can withstand before breaking is equal to the force
Similar Questions
In the figure, a 125 g ball on a 75.1 cm rope is swung in a vertical circle about a point 267 cm above the ground. If the ball is swung at the slowest speed where the ball goes over the top of the circle without the rope having any slack and the rope is released when the ball is at the top of the loop, how far to the right does the ball hit the floor?
A 0.300-kg object is swung in a circular path and in a vertical plane on a 0.500-m length string. If the angular speed at the bottom is 8.00 rad/s, what is the tension in the string when the object is at the bottom of the circle?Select one:a.23.52 Nb.25.08 Nc.41.34 Nd.9.6 Ne.12.54 N
A hockey puck with mass 180 g is attached to a rope of length 71.0 cm and swung in a horizontal circle against the ice at a rate of 89.0 rpm. Assuming the ice is frictionless, what is the tension in the rope? 2.01×103 N 4.00×104 N 1.01×103 N 11.1 N
A 0.440-kg pendulum bob passes through the lowest part of its path at a speed of 3.38 m/s.(a) What is the magnitude of the tension in the pendulum cable at this point if the pendulum is 77.0 cm long? N(b) When the pendulum reaches its highest point, what angle does the cable make with the vertical? (Enter your answer to at least one decimal place.) The correct answer is not zero.°(c) What is the magnitude of the tension in the pendulum cable when the pendulum reaches its highest point? Your response differs from the correct answer by more than 100%. N
A particle moves in a circle of radius 30 cm. Its linear speed is given by v = 2t, where t in second and v in m/s. Find out its radial and tangential acceleration at t = 3 s.A 220 m/s2, 50 m/s2 B 100 m/s2, 5 m/s2 C 120 m/s2, 2 m/s2 D 110 m/s2, 10 m/s2
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.