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 ]

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 ],

MARKS App · Accepted Answer

Using the conservation of linear momentum in the horizontal direction we get, 1 . 2 × 4 = 4 . 8 × v ⇒ v = 1 m s - 1 The loss in kinetic energy is equal to the amount of heat energy released. ∆ K = 1 2 × 1 . 2 × 5 2 - 1 2 × 4 . 8 × 1 2 ∆ K = 12 . 6 J

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