and d . d = d = = + + = unit ∴ cos θ = . , θ = cos – . Fig.
. (a) The scalar product of two vectors A and B is a scalar : A . B = A B cos θ . (b) B cos θ is the projection of B onto A .
(c) A cos θ is the projection of A onto B . u to be proportional to the speed of the drop but is otherwise undetermined. Consider a drop of mass . g falling from a height .
km. It hits the ground with a speed of . m s - . (a) What is the work done by the gravitational force ?
What is the work done by the unknown resistive force? Answer (a) The change in kinetic energy of the drop is ∆ = - = . J where we have assumed that the drop is initially at rest. Assuming that g is a constant with a value m/s , the work done by the gravitational force is, W g = mgh = - × × = .
J (b) From the work-energy theorem g r ∆ where W r is the work done by the resistive force on the raindrop. Thus W r = ∆ K − W g = . − = − . J is negative.
. WORK As seen earlier, work is related to force and the displacement over which it acts. Consider a constant force F acting on an object of mass m . The object undergoes a displacement d in the positive x -direction as shown in Fig.
An object undergoes a displacement d under the influence of the force F . . NOTIONS OF WORK AND KINETIC ENERGY: THE WORK-ENERGY THEOREM The following relation for rectilinear motion under constant acceleration a has been encountered in Chapter , v − u = as ( . )