A block weighing 90.0 N rests on a plane inclined at 25.0° to the horizontal. A
ID: 1440060 • Letter: A
Question
A block weighing 90.0 N rests on a plane inclined at 25.0° to the horizontal. A force F is applied to the object at 35.0° to the horizontal, pushing it upward on the plane. The coefficients of static and kinetic friction between the block and the plane are, respectively, 0.332 and 0.156.
(a) What is the minimum value of F that will prevent the block from slipping down the plane?
(b) What is the minimum value of F that will start the block moving up the plane?
(c) What value of F will move the block up the plane with constant velocity?
Explanation / Answer
given
w = 90 N
= 25°
= 35°
_static = 0.332
_dyn = 0.156
a)
static equilibrium both x and y axis. note x axis parallel with inclined plane and y axis perpendicular to it.
base principle of equilibrium;
Fy = 0
N + F sin ( - ) - w cos = 0
N = w cos - F sin ( - )...............(1)
Fx = 0
F cos ( - ) - w sin + f_static = 0
F cos ( - ) - w sin + _static N = 0.......(2)
remind of eqs (1), so eq (2) become
F cos ( - ) - w sin + _static (w cos - F sin ( - )) = 0
F(cos ( - ) - _static sin ( - )) = w(sin - _static cos )
F = w(sin - _static cos )/(cos ( - ) - _static sin ( - ))........(3)
F = 90(sin 25° - 0.332cos 25°)/(cos (35° - 25°) - 0.332 sin (35° - 25°))
F = 11.2543 N
b)
Fx = 0
F cos ( - ) - w sin - f_static = 0
F cos ( - ) - w sin - _static N = 0.......(4)
remind of eqs (1), so eq (4) become
F cos ( - ) - w sin - _static (w cos - F sin ( - )) = 0
F(cos ( - ) + _static sin ( - )) = w(sin + _static cos )
F = w(sin + _static cos )/(cos ( - ) + _static sin ( - ))........(5)
F = 90(sin 25° + 0.332 cos 25°)/(cos (35° - 25°) + 0.332 sin (35° - 25°))
F = 66.18 N
c)
Fx = 0
F cos ( - ) - w sin - f_dyn = 0
F cos ( - ) - w sin - _dyn N = 0.......(6)
remind of eqs (1), so eq (6) become
F cos ( - ) - w sin - _dyn (w cos - F sin ( - )) = 0
F(cos ( - ) + _dyn sin ( - )) = w(sin + _dyn cos )
F = w(sin + _dyn cos )/(cos ( - ) + _dyn sin ( - ))........(7)
F = 90(sin 25° + 0.156 cos 25°)/(cos (35° - 25°) + 0.156 sin (35° - 25°))
F = 51.57 N
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