Question

Two objects undergo a perfectly elastic collision. The velocity of object 1 before the collision is 2 m/s to the right. Object 2 is stationary before the collision. After the collision, object 1 is stationary. Which of the following statements is correct? Object 1 has a smaller mass than object 3

Objects 1 ans 2 have the same mass
Object 2 speed after the collision is smaller than speed of object 1 before the collision
Object 1 has a larger mass than object 2
Speed of object 2 after collision is larger than the speed of 1 before collision

Answer 1

Objects 1 and 2 have the same mass

Step-by-step explanation:

To solve this problem we apply the theory of shocks:

In an elastic shock the kinetic energy and the amount of linear movement or momentum are conserved.

Because the shock is elastic, the coefficient of elastic restitution (e) is equal to 1.

Principle of conservation of the momentum:

m1vi1+m2vi2=m1vf1+m2vf2 Equation 1

Formula to calculate the coefficient of elastic restitution (e):

e =( vf2- v1f)/ (Vi1- Vi2) Equation 2

Where

m1:mass of the object(1) in kg

m2:mass of the object(2) in kg

Vi1=Initial velocity of the m1 in m/s

Vf1=Final velocity of the m1 in m/s

Vi2=Initial velocity of the m2 in m/s

Vf2=Final velocity of the m2 in m/s

The initial velocity of the object1 is to the right, then, the sign is positive for the initial velocity of m1.

We assume that the object2 move to the right after the crash, so the sign is positive for the final speed of m2.

We know that vi1 = 2m / s, vi2 = 0, vf1 = 0, then, we replace this information in equation (1) :

We replace this information in equation (1) :

m1(2)+0=0+m2vf2

m1(2)- m2vf2=0 Equation 3

Equation 3

Because the shock is elastic, the coefficient of elastic restitution (e) is equal to 1,then , we replace this information in equation (2)

`1=(vf_(2)-0 )/(2-0)`

`1=(vf_(2) )/(2)`

`vf_(2) =2(m)/(s)`

We replace
`vf_(2) =2(m)/(s)` in the equation (3)

m1(2)- m2(2)=0

`2*m_(1) =2*m_(2)`

`m_(1) =(2)/(2) *m_(2)`

`m1=m2`

Answer: Objects 1 and 2 have the same mass