Question

If the coefficient of friction between a 500-gram mass and a rough board is 0.4, find the net force acting on the body when a) the board is horizontal and a pull of 100 grams is applied to the body; b) the board makes an angle of 30 degree with the horizontal. Assume force to be always parallel to the board.

Answer 1

Answer on question #64163, Physics / Mechanics — Relativity

Question If the coefficient of friction between a 500-gram mass and a rough board is 0.4, find the net force acting on the body when a) the board is horizontal and a pull of 100 grams is applied to the body; b) the board makes an angle of 30 degree with the horizontal. Assume force to be always parallel to the board.

Solution (a). There are four forces acting on mass. Along y-axis its gravitational force and reaction force from floor and they compensate each other. Along the x-axis there is 100 gran force and friction force. The friction force can be bigger then 100 gram, as

$F_{f}=\mu mg=500\cdot 9.8\cdot 0.4=200\cdot 9.8>100\cdot 9.8$

So, the friction force compensate the 100 gram force and hence total net force is zero.

(b). When there is 30 degree, we will have alomg the board

$F_{net}=mg\cos 30{}^{\circ}-\mu mg\sin 30{}^{\circ}=mg(\cos 30{}^{\circ}-\mu\sin 30{}^{\circ})\approx 0.67\cdot mg=333\,gram$