Question:

An object of mass $40\, kg$ and having a velocity $4\, m/s$ collides with another object $ \left( m=60\,kg \right) $ having velocity $2\, m/s$. The collision is perfectly inelastic. The loss in energy is:

Updated On: Jun 20, 2022
  • 110 J
  • 48 J
  • 392 J
  • 440 J
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is B

Solution and Explanation

When two bodies stick together after collision, then the collision is said to be perfectly inelastic.
In inelastic collision most of the kinetic energy is lost in other forms (specially as heat). Thus, in inelastic collision the kinetic energy is not conserved but total energy and momentum are conserved.
From law of conservation of momentum
$m_{1} \,u_{1}+m_{2}\, u_{2}=\left(m_{1}+m_{2}\right) v$
$40 \times 4+60 \times 2=(40+60) v$
$\Rightarrow v=\frac{280}{100}=2.8 \,m / s$
Decrease in kinetic energy
$=\frac{1}{2} m_{1}\, v_{1}^{2}+\frac{1}{2} m_{2}\, v_{2}^{2}-\frac{1}{2}\left(m_{1}+m_{2}\right) v^{2} $
$=\frac{1}{2} \times 40 \times(4)^{2}+\frac{1}{2} \times 60 \times(2)^{2}-\frac{1}{2}(40+60)(2.8)^{2}$
$=320+120-100 \times 3.92$
$=48 \,J .$
Note: It is not necessary that in inelastic collision, there is always a loss of kinetic energy. If in collision, the potential energy of a body is released then the kinetic energy would increase.
Was this answer helpful?
0
0

Concepts Used:

Work, Energy and Power

Work:

  • Work is correlated to force and the displacement over which it acts. When an object is replaced parallel to the force's line of action, it is thought to be doing work. It is a force-driven action that includes movement in the force's direction.
  • The work done by the force is described to be the product of the elements of the force in the direction of the displacement and the magnitude of this displacement.

Energy:

  • A body's energy is its potential to do tasks. Anything that has the capability to work is said to have energy. The unit of energy is the same as the unit of work, i.e., the Joule.
  • There are two types of mechanical energy such as; Kinetic and potential energy.

Read More: Work and Energy

Power:

  • Power is the rate at which energy is transferred, conveyed, or converted or the rate of doing work. Technologically, it is the amount of work done per unit of time. The SI unit of power is Watt (W) which is joules per second (J/s). Sometimes the power of motor vehicles and other machines is demonstrated in terms of Horsepower (hp), which is roughly equal to 745.7 watts.
  • Power is a scalar quantity, which gives us a quantity or amount of energy consumed per unit of time but with no manifestation of direction.