Two blocks with masses M1=8.50kg and M2=1.40kg are attached by a thin string which goes over a frictionless, massless pulley. M1 slides on an incline and there is friction between M1 and the incline. The incline is at an angle of 23.0 degrees from horizontal. M2 travels down at a constant velocity of 0.91m/s. Calculate the magnitude of the frictional force acting on M1.
To calculate the magnitude of the frictional force acting on M1, we can start by analyzing the forces acting on both blocks separately.
For M2, since it is moving down at a constant velocity, we can conclude that the net force acting on it is zero. This means that the gravitational force pulling it downward is balanced by the tension force in the string.
Now let's focus on M1. The forces acting on M1 are its weight (mg), the normal force (Fn), the parallel component of the gravitational force (mg.sinθ), and the frictional force (f). Here, θ is the angle of the incline.
We need to calculate the magnitude of the frictional force (f). Since M1 is on an incline and there is friction between M1 and the incline, we can state the following equation:
f = μ * Fn
where μ is the coefficient of friction and Fn is the normal force. The normal force can be found by taking the component of the gravitational force perpendicular to the incline, which is Fn = mg.cosθ.
To solve for μ, we need to find the acceleration of M1. We can use Newton's second law in the horizontal direction:
ΣF = ma
Here, the net force in the horizontal direction consists of the parallel component of the gravitational force (mg.sinθ) and the frictional force (f):
mg.sinθ - f = Ma
Substituting f = μ * Fn, we get:
mg.sinθ - μ * (mg.cosθ) = ma
Now we can solve for the acceleration (a).
Next, we can calculate the net force in the vertical direction for M1. The net force in the vertical direction consists of the component of the weight perpendicular to the incline (mg.cosθ) and the normal force (Fn):
ΣFy = mg.cosθ - Fn = 0
Solving for Fn, we get:
Fn = mg.cosθ
Finally, substitute Fn into the equation for the frictional force:
f = μ * Fn = μ * (mg.cosθ)
Now that we have found the expression for the frictional force, we can substitute the known values:
m1 = 8.50 kg
m2 = 1.40 kg
θ = 23.0 degrees
g = 9.8 m/s^2
v = 0.91 m/s
Using these values, you can calculate the magnitude of the frictional force acting on M1 by following the steps described above.