## Two balls collide with each other. Ball 1 experiences a high acceleration as a result of the collision, while Ball 2 experiences a small acc

Question

Two balls collide with each other. Ball 1 experiences a high acceleration as a result of the collision, while Ball 2 experiences a small acceleration. What can you conclude about Ball 2?

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6 months 2021-07-16T12:11:59+00:00 2 Answers 8 views 0

We conclude that ball 2 has a larger mass.

Explanation:

This is because the internal forces at collision are an action reaction pair. The force on ball 1 due to ball 2 equals the force on ball 2 due to ball 1. Since these forces are equal in magnitude, let’s denote it by F. So

For each ball, F = ma and a = F/m. Since F is the same for both balls, if follows that the acceleration of each ball is inversely proportional to its mass. That is, a ∝ 1/m.

Since ball 1 has a higher acceleration, it has a lower mass. Also ball 2 has a small acceleration, so it has a higher mass.

See explanation

Explanation:

Solution:-

– Denote the following:

mass of ball 1 = m1

initial velocity of ball 1 = vi,1

Final velocity of ball 1 = vf,1

mass of ball 2 = m2

initial velocity of ball 2 = vi,2

Final velocity of ball 2 = vf,2

– Since there are no external forces acting on the system containing the two balls then we can say that the linear momentum of the system is conserved.

– The conservation of linear momentum says that the momentum before or after the collision remains conserved:

Pi = Pf

Where,                        p = m*v

– The conservation of momentum for the given system:

m1*vi,1 + m2*vi,2 = m1*vi,1 + m2*vi,2

– Since no information is given about the initial conditions. We will consider the internal force (F) that acts when two balls come in contact. Then apply Newton’s second law of motion on both balls individually:

F = m*a

Where,             m: Mass of object

a: Acceleration of the object

– For ball 1:

F1 = m1*a1

– For ball 2:

F2 = m2*a2

Given that a1 > a2, and the the internal force that acts on both balls during collision obeys Newton’s 3rd Law i.e for every action there is an equal but opposite reaction: So , F1 = F2

F = m1*a1

F = m2*a2

m1*a1 = m2*a2

– Since, a1 > a2 for above equation to hold true then m1 < m2. That is the mass of ball 1 is quite less compared to ball 2.