Question

An inclined plane making an angle 30º with the horizontal is placed in a uniform horizontal electric field ɛ of 100 V/m (see figure). Particle of mass 1 kg and charge 0.01 C is allowed to slide down from rest from a height of 1 m. If the coefficient of friction is 0.2, find the time it will take the particle to reach the bottom.

Answer 1

The different forces on the particle are shown in figure.

From figure, N = mg cos 30º + qɛ cos 60º

Friction f = µN = µ mg cos 30º + µ qɛ  cos 60º 

Now the total force F acting along the inclined plane is

F = mg sin 30º – µ N – qɛ cos 30º 

or F = mg sin 30º – mg cos 30º – µqɛ cos 60º – qɛ cos 30º

Thus acceleration is

or a = F/m = g sin 30º  - µg cos 30º  - µqɛ /m cos 60º  - qɛ/m cos30º

Now, distance travelled in time t is