Theory question 107
DynamicsThe position vector of a particle of mass 3 kg moving along a space curve is given by r = (4t3 − t2)i − (2t2 − t)j at any time t seconds. Find the force acting on it at t = 2 seconds.
Show the model answer
Model answer
v = dr/dt = (12t2 − 2t)i − (4t − 1)j
a = dv/dt = (24t − 2)i − 4j
At t = 2: a = 46i − 4j
F = ma = 3(46i − 4j) = (138i − 12j) N (magnitude ≈ 138.5 N)
Explanation
Differentiate twice to get acceleration, then use F = ma.