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Prof. K. tried to devise an easier way of throwing a ball for her dog. The ball B has a mass of 0.5 kg and is restricted to move inside a frictionless slot. The rotation of the arm OA causes the ball to move. The rod is rotating with a constant angular velocity of 2 rad/s and the angle e = 30°. Assume the ball only touches the bottom of the slot and doesn't spin. a) Clearly define your system using polar coordinates. b) Compute the velocity of the ball relative to point O (in m/s). Express your answer in polar coordinates. Hint: Use the information you know about the direction of the velocity of the ball to help you eliminate unknown variables. If it makes it easier, transform between polar and rectangular coordinates here, but express your final answer in polar coordinates. [Ans. to Check: 0.666 m/s e,] c) Compute the acceleration of the ball relative to point O (in m/s²). Express your answer in polar coordinates. The same hint from part (b) applies. [Ans. to Check: 3.846 m/s² e] d) Calculate the true acceleration of the ball in m/s². Express your answer in rectangular coordinates. [Ans. to Check: 3.076 m/s² i] e) Draw an FBD and IRD of the ball. Determine the force felt by the ball. Express your answer using the rectangular coordinates shown. [Ans. to Check: 1.54 N i] e =2 rad/s- 0.5 m

Prof. K. tried to devise an easier way of throwing a ball for her dog. The ball B has a mass of 0.5 kg and is restricted to move inside a frictionless slot. The rotation of the arm OA causes the ball to move. The rod is rotating with a constant angular velocity of 2 rad/s and the angle e = 30°. Assume the ball only touches the bottom of the slot and doesn't spin. a) Clearly define your system using polar coordinates. b) Compute the velocity of the ball relative to point O (in m/s). Express your answer in polar coordinates. Hint: Use the information you know about the direction of the velocity of the ball to help you eliminate unknown variables. If it makes it easier, transform between polar and rectangular coordinates here, but express your final answer in polar coordinates. [Ans. to Check: 0.666 m/s e,] c) Compute the acceleration of the ball relative to point O (in m/s²). Express your answer in polar coordinates. The same hint from part (b) applies. [Ans. to Check: 3.846 m/s² e] d) Calculate the true acceleration of the ball in m/s². Express your answer in rectangular coordinates. [Ans. to Check: 3.076 m/s² i] e) Draw an FBD and IRD of the ball. Determine the force felt by the ball. Express your answer using the rectangular coordinates shown. [Ans. to Check: 1.54 N i] e =2 rad/s- 0.5 m

International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter7: Dry Friction
Section: Chapter Questions
Problem 7.11P: Solve Prob. 7.10 assuming that the pick-up truck has front-wheel drive.
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Prof. K. tried to devise an easier way of throwing a ball for her dog. The ball B has a mass of 0.5 kg and is restricted to move inside a frictionless slot. The rotation of the arm OA causes the ball to move. The rod is rotating with a constant angular velocity of 2 rad/s and the angle 0 = 30°. Assume the ball only touches the bottom of the slot and doesn't spin. a) Clearly define your system using polar coordinates. b) Compute the velocity of the ball relative to point O (in m/s). Express your answer in polar coordinates. Hint: Use the information you know about the direction of the velocity of the ball to help you eliminate unknown variables. If it makes it easier, transform between polar and rectangular coordinates here, but express your final answer in polar coordinates. [Ans. to Check: 0.666 m/s e] c) Compute the acceleration of the ball relative to point O (in m/s?). Express your answer in polar coordinates. The same hint from part (b) applies. [Ans. to Check: 3.846 m/s? e] d) Calculate the true acceleration of the ball in m/s². Express your answer in rectangular coordinates. [Ans. to Check: 3.076 m/s² i] e) Draw an FBD and IRD of the ball. Determine the force felt by the ball. Express your answer using the rectangular coordinates shown. [Ans. to Check: 1.54 N i] B. e = 2 rad/s 0.5 m
Transcribed Image Text:Prof. K. tried to devise an easier way of throwing a ball for her dog. The ball B has a mass of 0.5 kg and is restricted to move inside a frictionless slot. The rotation of the arm OA causes the ball to move. The rod is rotating with a constant angular velocity of 2 rad/s and the angle 0 = 30°. Assume the ball only touches the bottom of the slot and doesn't spin. a) Clearly define your system using polar coordinates. b) Compute the velocity of the ball relative to point O (in m/s). Express your answer in polar coordinates. Hint: Use the information you know about the direction of the velocity of the ball to help you eliminate unknown variables. If it makes it easier, transform between polar and rectangular coordinates here, but express your final answer in polar coordinates. [Ans. to Check: 0.666 m/s e] c) Compute the acceleration of the ball relative to point O (in m/s?). Express your answer in polar coordinates. The same hint from part (b) applies. [Ans. to Check: 3.846 m/s? e] d) Calculate the true acceleration of the ball in m/s². Express your answer in rectangular coordinates. [Ans. to Check: 3.076 m/s² i] e) Draw an FBD and IRD of the ball. Determine the force felt by the ball. Express your answer using the rectangular coordinates shown. [Ans. to Check: 1.54 N i] B. e = 2 rad/s 0.5 m
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