Problem 62GP

A 0.145-kg baseball pitched horizontally at 35.0 m/s strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.

Solution 62GPIntroductionWe need to calculate linear acceleration first from the given data and then we can calculatethe time required by using the value of distance given.Step 1:Diameter of the pulley = 50 cmRadius r = 0.25 mMass of the pulley m = 2.0 kg 1 2 2So, its moment of inertia I = 2 × 2.0 kg × (0.25) kg.m 2I = 0.0625 kg.m …..(1)Let T be the tension on the rope 1So, T 1.5g = 1.5a ( a is linear acceleration) 1T 1 = 1.5g + 1.5a…..(2)Given that, T 2 = 10 N …..(3)Torque due to T = = 0.25 m × 10 N (from equation (3)) 2 2 2 = 2.5 N.mTorque due to tension T 1 = 0.25 m × (1.5g + 1.5a)(from equation (2)) 1Therefore, net torque = 2 1 = 2.5 N.m 0.25 m × (1.5g + 1.5a)…..(4)