A 12.0 kg object is on a surface that is inclined 30 degrees and the coefficient of friction is 0.65.
Determine the force of static friction if the block remains stationary.
Assuming 0.65 is the coefficient of static friction, u.
If you resolve forces acting perpendicular to the ramp, with the direction of the normal force as positive:
Fn - mg*cos30 = 0
Fn - (12)(9.81)*cos30 = 0
Fn = 101.95 N
Then:
Fs = u * Fn
Fs = 0.65 (101.95)
Fs = 66.3 N
Check the opposing force:
mg*sin30
= (12)(9.81)*sin30
= 58.86 N
58.86 N < 66.3 N, which makes sense, because the question states that the block remains stationary ( i.e., there is not enough of an opposing force to overcome the force of static friction).
Ff = μ m g cos(30º)
To determine the force of static friction if the block remains stationary, we need to understand the forces acting on the object and use the concept of equilibrium.
First, let's identify the forces acting on the object:
1. Weight (mg): This is the force due to gravity and can be calculated as the mass (m) of the object multiplied by the acceleration due to gravity (g ≈ 9.8 m/s²).
Weight = mg
2. Normal force (N): This is the force exerted by the surface perpendicular to the object. It can be calculated as the component of the weight acting perpendicular to the incline.
Normal force = mg cosθ, where θ is the angle of inclination (θ = 30°).
3. Force of friction (f): This is the force that opposes the motion or potential motion. There are two types of friction forces: static friction and kinetic (or sliding) friction. Since the block remains stationary, we are interested in the force of static friction.
The force of static friction can be calculated using the equation:
f = μsN, where μs is the coefficient of static friction and N is the normal force.
Given:
Mass of the object (m) = 12.0 kg
Angle of inclination (θ) = 30°
Coefficient of static friction (μs) = 0.65
Let's calculate the normal force (N) first:
Normal force = mg cosθ
= (12.0 kg)(9.8 m/s²) cos(30°)
Now, we can calculate the force of static friction (f):
Force of static friction = μsN
= (0.65)(Normal force)
By plugging in the values, we can find the force of static friction.