Question

"A parcel moving in a horizontal direction with speed v0 = 13 m/s breaks into two fragments of weights 1.4 N and 1.9 N, respectively. The speed of the larger piece remains horizontal immediately after the separation and increases to v1.9 = 29 m/s. Find the necessary speed and direction of the smaller piece immediately after the separation. (Assume the initial direction of the parcel is positive. Indicate the direction with the sign of your answer.)"

Answer 1

the smaller particle moves with speed of 8.706 m/s in the opposite direction to the bigger particle.

Step-by-step explanation:

Speed of the original particle = 13 m/s

We designate particles as A and B

The final weights of the component particles are

Particle A = 1.4 N

particle B = 1.9 N

The speed of the larger piece (particle B) = 29 m/s

We know that weight is the product of a body's mass and acceleration due to gravity g which is equal to 9.81 m/s^2, therefore, masses of the particles are

particle A = 1.4/9.81 = 0.143 kg

Particle B = 1.9/9.81 = 0.194 kg

The momentum of a body is the product of its mass and its velocity i.e

P = mv

This means that the mass of the particle before splitting is

0.143 kg + 0.194 kg = 0.337 kg

Momentum of the initial whole particle = mv

==> 0.337 x 13 = 4.381 kg-m/s

The bigger particle B remains horizontal, and has a momentum of

mv = 0.194 x 29 = 5.626 kg-m/s

According to the conservation of momentum, the total initial momentum of a system must be equal tot the total final momentum of the system.

Initial total momentum of the system = 4.381 kg-m/s (momentum of original particle before splitting)

Final total momentum of the system = Total momentum of the particles after splitting = 5.626 kg-m/s + ( 0.143 kg x
`V_(B)`)

where
`V_(B)` is the velocity of smaller particle A

final total momentum of the system = 5.626 + 0.143
`V_(B)`

Equating the two momenta of the system, we'll have

4.381 = 5.626 + 0.143
`V_(B)`

4.381 - 5.626 = 0.143
`V_(B)`

-1.245 = 0.143
`V_(B)`

`V_(B)` = -1.245/0.143 = -8.706 m/s

The negative sign indicates that the smaller particle moves in the opposite direction to the bigger particle