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A large truck of mass 4M is traveling at a speed of V when it collides with a small car of mass M that is at rest. The truck and car stick together after the collision. When the truck and car stuck together after the collision, the speed of the center of mass of the truck-car system is Vf. If the truck and car have an elastic collision, the speed of the center of mass of the truck-car system is Vf2. Which of the following expressions for Vf2 must be true?

a. 4/5 V
b. 1/5 V
c. V
d. 5/4 V
e. 5V

Sagot :

Answer: (a)

Explanation:

Given

Mass of large truck is 4M with velocity V

Mass of small car is M which is at rest

After the collision car and truck stick together

Conserving momentum

[tex]\Rightarrow 4MV+M(0)=5M\times V_f\\\\\Rightarrow V_f=\dfrac{4}{5}V[/tex]

For elastic collision, the velocity of the center of mass remains the same as the momentum is conserved and there is no acceleration involved.

So, for elastic collision velocity [tex]V_f_2=\frac{4}{5}V[/tex]

As a result of collision when there is no loss in the kinetic energy of the object then the collision is said to be elastic and the kinetic energy and the momentum of the objects are conserved.

The momentum is written as:

[tex]\rm m_{1}v_{1}+m_{2}v_{2} = m_{1}v_{1}'+m_{2}v_{2}'[/tex]

Where, mass = m and velocity = v

The following option is true:

Option a.  [tex]\dfrac{4}{5} \rm V[/tex]

The momentum can be estimated by:

Given,

  • Mass of large truck = 4M

  • Mass of small car = M

  • The velocity of truck = V

After the collision the conserving momentum will be:

[tex]\begin{aligned}\rm 4MV + M(0) &= 5\rm M \times V_{f}\\\\\rm V_{\rm f} &= \dfrac{4\rm MV}{5\rm M}\\\\\rm V_{f} &= \dfrac{4}{5V}\end{aligned}[/tex]

There will be no acceleration as the momentum is conserved and the center of mass is the same.

Therefore, elastic collision will have a momentum of  [tex]\dfrac{4}{5} \rm V[/tex].

To learn more about momentum and elastic collision follow the link:

https://brainly.com/question/8169285

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