A ball of mass m and radius r rolls along the ground without slipping. It experiences...

 

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A ball of mass m and radius r rolls along the ground without slipping. It experiences a drag force due to air resistance of D = -bv where v is the velocity of the ball and b is a constant. You may assume that the moment of inertia of the ball about a rotation axis passing through its centre is /= 0.4mr (a) Apply Newton's laws of motion to show that the acceleration of the ball is 5bv 7m a = (b) If m= 100 g, b = 0.1 Ns/m and v = 2 m/s, calculate how long it will take for the ball's velocity to halve. Show all steps in your working. (c) Explain why you would expect the drag force to cause the ball to decelerate more quickly if it was sliding (ie, moving without rotating) rather than rolling. A ball of mass m and radius r rolls along the ground without slipping. It experiences a drag force due to air resistance of D = -bv where v is the velocity of the ball and b is a constant. You may assume that the moment of inertia of the ball about a rotation axis passing through its centre is /= 0.4mr (a) Apply Newton's laws of motion to show that the acceleration of the ball is 5bv 7m a = (b) If m= 100 g, b = 0.1 Ns/m and v = 2 m/s, calculate how long it will take for the ball's velocity to halve. Show all steps in your working. (c) Explain why you would expect the drag force to cause the ball to decelerate more quickly if it was sliding (ie, moving without rotating) rather than rolling.

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