A window washer pushes his scrub brush →−
up a vertical window at constant speed by applying a force F as
shown in Fig. P5.74. The brush weighs 15.0 N and the coefficient
of kinetic friction is μk = 0.150. Calculate (a) the magnitude of →−
the force F and (b) the normal force exerted by the window on the brush.
where's the picture?
any how, F=uN
brush weighs 15N , 15N=the normal force if the washer doesn't push down. If he/she did push down on the brush with a force F, it would be the cosine of the angle that is pushing down . so yeah draw a free body, and you'll see which forces are required
I don't understand your symbology →−
F*sin(theta) = F*cos(theta) * (mew) + weight
F*sin(theta) = F*cos(theta) * (0.150) + 15
Fsin(theta) - 15 - (Uk)N=0
Fsin(theta) - (.150)Fcos(theta)= 15
Plug in theta and solve for F. Once you get F use equation
Fcos(theta)-N=0 to solve for N
To calculate the magnitude of the force F, we need to consider the forces acting on the scrub brush. In this case, we have two forces: the force F applied by the window washer and the force of kinetic friction.
(a) To find the magnitude of the force F, we need to balance the forces in the vertical direction:
Sum of forces in the vertical direction = 0
The only vertical force acting on the scrub brush is its weight, which is given as 15.0 N. Therefore, the magnitude of force F applied by the window washer must be equal to the weight of the brush:
Magnitude of force F = Weight of the brush = 15.0 N
(b) To calculate the normal force exerted by the window on the brush, we need to consider the forces in the horizontal direction.
The force of kinetic friction can be calculated using the formula:
Force of kinetic friction = coefficient of kinetic friction * Normal force
We know that the coefficient of kinetic friction (μk) is given as 0.150. We want to find the normal force.
To calculate the normal force, we use the fact that the sum of the forces in the horizontal direction is zero:
Sum of forces in the horizontal direction = 0
The only horizontal force acting on the brush is the force of kinetic friction. Therefore, the force of kinetic friction must be equal in magnitude but opposite in direction to the applied force F:
Force of kinetic friction = Magnitude of force F
Now we can substitute these values into the formula for the force of kinetic friction:
Force of kinetic friction = 0.150 * Normal force
Since the force of kinetic friction is equal in magnitude to the applied force F, we can rewrite it as:
0.150 * Normal force = 15.0 N
Solving for the normal force:
Normal force = 15.0 N / 0.150
Normal force = 100 N
Therefore, the normal force exerted by the window on the brush is 100 N.
F is 208.42N normal is 125.14 N
v=const => a=0
N =F(x)•cosα
F(y)•sinα=mg+F(fr)
F(y)=(mg+μN)/sinα
F=sqrt(F(x)²+F(y)²)