Question

Two spheres are moving towards each other. Both have the same radius but their masses are 2kg and 4kg. If their velocities are 4m/s and 2m/s respectively and coefficient of restitution is e=1/3. Find:
(a) their common velocity along the line of impact
(b) final velocities along line of impact
(c) impulse of deformation
(d) impulse of reformation
(e) maximum potential energy of deformation
(f) loss in kinetic energy due to collision

Answer 1

Answer:

Hii CutiePie

Let v1 and v2 be the final velocities of A and B respectively then by conservation of momentum along line of impact.

m1u1+m2u2=m1v1+m2v2

2(4cos30∘)−4(2cos30∘)=2(v1)+4(v2)

or 0=v1+2v2....(1)

By Newton's Experimental Law.

2(2cos30∘)−4(2cos30∘)=2(v1)+4(v2)

or 0=v1+2v2....(1)

By Newton's Experimental Law,

e=velocity of separation along LOCvelocity of approachalong LOC

or 13=v2−v14cos30∘+2cos30∘

or v2−v1=3–√ ...(2)

From the above two eqations,

v1=−23–√m/s

Negative answer denotes that we have chosen the wrong direction, actual direction of final velocity will be opposite to the direction we assumed in figure

v2=13–√m/s

PLZ FOLLOW ME

Explanation:

Answer 2

Answer:

Hii CutiePie

Let v1 and v2 be the final velocities of A and B respectively then by conservation of momentum along line of impact.

m1u1+m2u2=m1v1+m2v2

2(4cos30∘)−4(2cos30∘)=2(v1)+4(v2)

or 0=v1+2v2....(1)

By Newton's Experimental Law.

2(2cos30∘)−4(2cos30∘)=2(v1)+4(v2)

or 0=v1+2v2....(1)

By Newton's Experimental Law,

e=velocity of separation along LOCvelocity of approachalong LOC

or 13=v2−v14cos30∘+2cos30∘

or v2−v1=3–√ ...(2)

From the above two eqations,

v1=−23–√m/s

Negative answer denotes that we have chosen the wrong direction, actual direction of final velocity will be opposite to the direction we assumed in figure

v2=13–√m/s

PLZ FOLLOW ME

Explanation: