A projectile of mass 1 . 2 kg undergoes a perfectly inelastic collision with a trolley of mass 3 . 6 kg as shown in the figure. At the time of the collision, the speed of the projectile is 5 m s - 1 at an angle of 37 ° with the horizontal. The trolley is free to move, only along a horizontal rail…

Question

A projectile of mass 1 . 2 kg undergoes a perfectly inelastic collision with a trolley of mass 3 . 6 kg as shown in the figure. At the time of the collision, the speed of the projectile is 5 m s - 1 at an angle of 37 ° with the horizontal. The trolley is free to move, only along a horizontal rail which coincides with the direction of the projectile's horizontal motion. Assuming that the trolley doesn't topple, calculate the amount of heat energy (in J ) released in the collision. [Take sin 37 ° = 3 5 and cos 37 ° = 4 5 ]

Aicharya · Accepted Answer

Using the conservation of linear momentum in the horizontal direction we get,

$1.2 \times 4 = 4.8 \times v$

$\Rightarrow v = 1 m s^{- 1}$

The loss in kinetic energy is equal to the amount of heat energy released.

$|∆ K| = \frac{1}{2} \times 1.2 \times {(5)}^{2} - \frac{1}{2} \times 4.8 \times {(1)}^{2}$

$|∆ K| = 12.6 J$

A projectile of mass 1 . 2 kg undergoes a perfectly inelastic collision with a trolley of mass 3 . 6 kg as…

Solution