An IIT level question:-
A beagle of mass m = 4 kg runs from the left end of a curved ramp with speed
V=8 m/s at height 8 m above the ground. It then slides to the right and comes to rest when it reaches a height 10 m from
the ground. The maximum increase in thermal energy of the beagle -ramp system because of sliding
is (g = 10 m/s^2)
Answers
A beagle of mass m = 4 kg runs from the left end of a curved ramp with speed v₀ = 8 m/s at height 8 m above the ground. It then slides to the right and comes to rest when it reaches a height 10 m from the ground.
The maximum increase in thermal energy of the beagle -ramp system because of sliding is ..
At first we should find the total energy at both positions.
Total mechanical energy of beagle at h = 8m,
= potential energy + kinetic energy
= mgh + 1/2 mv₀²
= 4 kg × 10 m/s² × 8 m + 1/2 × 4 kg × (8m/s)²
= 320 + 128
= 448 J
Total mechanical energy of beagle at H = 10 m,
= potential energy + kinetic energy
= mgH + 1/2 mv²
= 4 kg × 10 m/s² × 10 m + 1/2 × 4 kg × (0 m/s)²
= 400 J + 0
= 400 J
According to Work-Energy theorem,
change in total mechanical energy is the work done which is converted in thermal energy = 448 J - 400 J = 48 J.