Saved Bookmarks
| 1. |
A particle is kept at rest at the origin. A constant force rarr F starts acting on it at t =0 . Find the speed of the particle at time t. |
|
Answer» SOLUTION :The equation of motion is . `rarr dp / dt = rarr F` As the particle starts from rest and the force is always in the same direction, the motion will be along this direction, THUS, we can write `dp/ dt = F ` or, `(int_(0)^(P) dp = int_(0)^(t) F dt)` ` p = Ft` or, ` m_0 V / (sqrt 1-v^(2) / c^(2)) = Ft ` or, `m_(0) ^(2) V^(2) = F^(2) t^(2) - F^(2) t^(2) / C^(2)V^(2)` V^(2) (m_(0)^(2) + F^(2) t^(2)/ C^(2)) = F^(2) t^(2)` or, `V = Ftc / (sqrt m_(0) ^(2) C^(2) + F^(2) t^(2)) ` Note from example (47.4)that however large t MAY be , V can never EXCEED c, No matter how long you apply a force , the speed of a particl will be less than the speed c. |
|