The Figure shows the result of a collision of a 4.00 kg ball with an object loca

Question

The Figure shows the result of a collision of a 4.00 kg ball with an object located at the origin. The position of the objects are shown at 3.4 s intervals. What is the mass of the object that was originally located at the origin?

What is the change in the kinetic energy as a result of the collision?

8.[1pt] The Figure shows the result of a collision of a 4.00 kg ball with an object located at the origin. The position of the objects are shown at 3.4 s intervals. What is the mass of the object that was originally located at the origin? -2 x (m)

Explanation / Answer

Initial speed of mass 1,

v1 =( 1/3.4)m/s (For 1 interval)

Final speed of mass 1,

v1' = root(2.9^2+ 1.7^2)/4*3.4 = 0.84 /3.4 m/s ( for 4 interval)

Initial speed of the object, mass-2,

v2 =0

FInal speed of mass 2,

v2' = root(1.25^2+1.9^2)/8*3.4 =0.284/3.4 m/s(for 8 intervals)

now , using conservation of momentum,

m1*v1+m2*v2=m1*v1'+m2*v2'

4*1/3.4 + 0 = 0.84/3.4*14 +m2*0.284/3.4

4*1 = 0.84*1.75 +m2*0.284

m2 =2.254 Kg approaximately.

Change in kinetic energy collision,

= 1/2*m*v1^2 -1/2m*v1'^2 -1/2m2*v2'^2

=1/2*4*(1/3.4)^2 -1/2*4*(0.84/3.4)^2-1/2*2.254*(0.284/3.4)^2

= 1/2*4*(1/3.4)^2 -1/2*4*(0.84/3.4)^2-1/2*2.254*(0.284/3.4)^2

=0.173 -0.122 -7.863*10^-3

= 0.04313 J (approax)

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