a window easher pushes his brush up a vertical window at constant velocity by applying a force F as shown below. The brush weighs 12 N and the coefficient of the kinetic friction is 0.2. find the magnitude of force F.
To find the magnitude of force F, we need to analyze the forces acting on the brush. There are two main forces involved: the force applied by the window washer (F) and the force of kinetic friction (fk). We can set up an equation using Newton's second law:
ΣF = ma
Since the brush is moving at constant velocity, the acceleration (a) is zero. Therefore, the net force (ΣF) acting on the brush must also be zero. This allows us to write the equation as:
F - fk = 0
The force of kinetic friction (fk) can be calculated using the formula:
fk = μk * N
where μk is the coefficient of kinetic friction and N is the normal force. The normal force (N) is the weight of the brush, which is equal to its mass (m) multiplied by the acceleration due to gravity (g):
N = mg
Given that the weight of the brush is 12 N, we can substitute this value in the equations. The equation now becomes:
F - μk * mg = 0
Substituting the value of the coefficient of kinetic friction (μk = 0.2) and the weight of the brush (mg = 12 N), we have:
F - 0.2 * 12 = 0
Simplifying the equation gives us:
F - 2.4 = 0
To isolate F, we can add 2.4 to both sides of the equation:
F = 2.4
Therefore, the magnitude of force F is 2.4 N.