1. Consider an elastic collision in one dimension that involves objects of mass

Question

1. Consider an elastic collision in one dimension that involves objects of mass m1=4 kg and m2=19 kg. The larger mass is initially at rest, and the smaller one has an initial velocity of 15 m/s. Find the final velocities of the two objects after the collision.

v1f

v2f

2. A bullet (m = 0.0250 kg) is fired with a speed of 91.00 m/s and hits a block (M = 2.80 kg) supported by two light strings as shown, stopping quickly. Find the height to which the block rises.

Find the angle (in degrees) through which the block rises, if the strings are 0.530 m in length.

Explanation / Answer

1.

m1=4kg , m2=19kg , v1i =15m/s , v2i=0 m/s

Use equations,

v1f= [(m1-m2)/(m1+m2)]v1i = [(4-19)/(4+19]*15 = -0.052m/s ………………..directed left

v2f=[ (2m1)/(m1+m2)]v1i=[(2*4)/(4+19)]*15 = 5.2m/s ----------------------directed right

2.

By law of conservation of momentum

m1v1+m2v2= (m1+m2)Vc               ………………..Vc is common velocity since bullet stuck in the block

v2=0m/s

Vc= m1v1/(m1+m2) = (0.0250*91.0)/(0.0250+2.80) = 0.805m/s

By law of conservation of energy

KE of combined mass = PE of combined mass

½*(m1+m2)*Vc^2 = (m1+m2)*g*h

1/2*(0.0250+2.80)*0.805^2 = (0.0250+2.80)*9.8*h         => h= 0.033m =3.3cm

Use equation,

q= cos^-1[(L-h)/L) = cos^-1[(0.530-0.033)/0.53] = 20.33 deg

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