A12.1 g object moving to the right at 21 cm/s overtakes and collides elastically with a 13.1 g object moving in the same direction at 11.2 cm/s. (a) find the velocity of the 12.1 g object after the collision. answer in units of cm/s. (b) find the velocity of the 13.1 g object after the collision. answer in units of cm/s.

The 12.1g mass moves at a speed of 10.81 cm/s after the crash and the 12.1g mass moves at a speed of 20.61 cm/s after the crash.

Both masses move to the right because the sign was positive.

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):

  Equation 2

m1=12.1 g ,  

Vi1= 21cm/s : Initial velocity of the m1

m2=13.1 g  

Vi2=11.cm/s: Initial velocity of the m1

v1f: Final velocity of the m1

vf2: Final velocity of the  m2

The initial velocities of both masses are to the right then the sign is positive.

We assume that both masses move to the right after the crash, so the sign is positive for the final speeds of both masses.

We replace this information in equation (1) :

12.1 * 21 + 13.1 * 11.2 = 12.1 * vf1 + 13.1 * vf2  

254.1 + 146.72 = 12.1 * vf1 + 13.1 * vf2  

400.82 = 12.1 * vf1 + 13.1 * vf2  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)

9.8 = vf2 - vf1 Equation (4)

Vf2 = vf1 + 9.8 Equation (5)

We replace the equation 5 in the equation (3)

400.82 = 12.1vf1 + 13.1( vf1 + 9.8 )  Equation (3)

400.82 = 12.1vf1 + 13.1vf1 + 13.1 * 9.8  

400.82 = 25.2vf1 + 128.38  

400.82 - 128.38 = 25.2vf1

272.44 = 25.2vf1

vf1 = (272.44) / (25.2)

vf1 = 10.81 cm/s

We replace vf1 = 10.81 cm/s in the equation (5):

Vf2 = 10,81 + 9.8  

Vf2 = 10,81 + 9.8  

Vf2 = 20.61cm/s  

The 12.1g mass moves at a speed of 10.81 cm / s after the crash and the 12.1g mass moves at a speed of 20.61 cm/s after the crash.

Both masses move to the right because the sign was positive.

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