Question 2.6.9: A force F varies with time according to F = 4 + 12t, where F...
A force F varies with time according to F = 4 + 12t, where F is in newtons and t in seconds. The force acts on a block of mass m = 2.00 kg, which is initially at rest on a frictionless horizontal surface. F makes an angle of 30° with the horizontal (see Figure 6.8). When will the force lift the body from the table? What will the velocity of the body be at that instant?
The block will leave the table when the normal reaction force R becomes zero.
R + F sin30° = mg
so
F = 40 N when R = 0.
This happens when t = 3.0 s. The horizontal component of F is
(4 + 12 t) cos30° = 3.64 + 10.39t
The change in the body’s momentum in the horizontal direction is the area under the F_{x} versus t graph from t = 0 to t = 3.0 s. This area is 57.7 N s. Thus, the horizontal component of velocity is 28.8 m s^{-1}. The vertical component is zero.