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1. A ball of mass 2m moving to the right at speed 2v suffers a head-on completely elastic collision with a ball of mass m which is also initially moving to the right at a speed v. Find the speed of the larger mass after the collision. Call the larger mass M. Let the final speeds be Va and Vb to the right for the smaller and larger masses respectively.From momentum conservation: M(2v)+mv = mVa + MVbFor 1-D elastic: 2v v = Va Vb i.e. v = Va-VbSo M(2v) = MVb + mVbVb = (2Mv)/(M+m)Version 1: M= 2m Vb = 4v/3Version 2: M= 3m Vb = 3v/2Version 3: M= 4m Vb = 8v/5Version 4: M= 5m Vb = 5v/3

vhd2. A block of mass M = 1kg sits at the edge of a table. It is struck by a bullet of mass m = 5 g moving at speed v = 100 m/s, which becomes embedded in the block. The block lands a distance d = 25 cm from the edge of the table. Find the speed of the block+bullet when it hits the ground.By momentum conservation: mv = (m+M) VfVf = mv/(m+M) = .5 m/sTime of fall t = d/Vf = d(m+M)/mvVertical velocity Vfy = gt = gd(m+M)/mv = 4.9 m/sTotal speed = ( Vf2 + Vfy2 )Version 1: M = 1kg, d = 25 cm, m = 5g, v = 100 m/s, Total speed = 4.93 m/sVersion 2: M = 1kg, d = 25 cm, m = 1g, v = 500 m/s, Total speed = 4.93 m/sVersion 3: M = 1kg, d = 25 cm, m = 2g, v = 250 m/s, Total speed = 4.93 m/sVersion 4: M = 1kg, d = 25 cm, m = 4g, v = 125 m/s, Total speed = 4.93 m/s

3. A solid sphere rotates about a point on its edge as shown. The sphere has mass M = 100 g and radius R = 2 cm. (a) Find the moment of inertia around the axis of rotation.(b) The sphere is released from rest in a vertical position. What is its angular velocity at the lowest point?

Around the center the moment of inertia is (2/5) MR2.(a) By the parallel axis theorem, the new moment of inertia is I = (2/5) MR2+ MR2 = (7/5) MR2.(b) By conservation of energy I = Mg (2R) = (20/7) (g/R)Version 1: M = 100g, R = 2cm, I = 5.6 x 10-5 kg m2, = 37.4 rad/sVersion 2: M = 50g, R = 2cm, I = 2.8 x 10-5 kg m2, = 37.4 rad/sVersion 3: M = 100g, R = 1cm, I = 1.4 x 10-5 kg m2, = 52.9 rad/sVersion 4: M = 50g, R = 1cm, I = 0.7 x 10-5 kg m2, = 52.9 rad/s