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.
Fo = M*g = 12 * 9.8 = 117.6 N. = Force of the object.
Fp = 117.6*sln30 = 58.8 N. =
Force parallel to the incline.
Fn = 117.6*Cos30 = 101.8 N. = Normal force.
Fs = u*Fn = 0.65 * 101.8 = 66.2 N. - Force of static friction.
To determine the force of static friction, we need to use the equation:
Fs ≤ μs * Fn
where:
Fs is the force of static friction,
μs is the coefficient of static friction,
Fn is the normal force.
First, let's calculate the normal force. The normal force is the force exerted by a surface to support the weight of an object resting on it and is perpendicular to the surface. In this case, it will be the component of the gravitational force acting perpendicular to the inclined surface.
Fn = m * g * cos(θ)
where:
m is the mass of the object,
g is the acceleration due to gravity (approximated as 9.8 m/s²),
θ is the angle of inclination (30 degrees).
Let's substitute the given values into the equation:
Fn = 12.0 kg * 9.8 m/s² * cos(30°)
Now, calculate Fn:
Fn = 12.0 kg * 9.8 m/s² * 0.866
Fn = 101.09 N
Next, we can calculate the force of static friction (Fs):
Fs ≤ μs * Fn
Substituting the given coefficient of static friction (μs = 0.65) and the calculated normal force (Fn = 101.09 N) into the equation:
Fs ≤ 0.65 * 101.09 N
Now, solve for Fs:
Fs ≤ 65.71 N
Therefore, the force of static friction (Fs) must be less than or equal to 65.71 N to keep the block stationary.
To determine the force of static friction, we need to calculate the maximum force of static friction that can act on the object to keep it stationary.
The maximum force of static friction (Ffs) can be calculated using the following formula:
Ffs = μs * N
Where:
- Ffs is the force of static friction
- μs is the coefficient of static friction
- N is the normal force
The normal force (N) can be calculated by analyzing the forces acting on the object. Since the object is on an inclined surface, we need to consider the gravitational force and its component along the inclined plane.
The gravitational force vector (Fg) can be decomposed into two components:
- The component parallel to the inclined plane: Fg_parallel = m * g * sin(θ)
- The component perpendicular to the inclined plane: Fg_perpendicular = m * g * cos(θ)
Where:
- m is the mass of the object (12.0 kg)
- g is the acceleration due to gravity (9.8 m/s²)
- θ is the angle of inclination (30°)
The normal force (N) is equal and opposite to the perpendicular component of the gravitational force. Thus, N = Fg_perpendicular = m * g * cos(θ).
Now, substituting the given values into the equations:
m = 12.0 kg
g = 9.8 m/s²
θ = 30°
μs = 0.65
Fg_perpendicular = m * g * cos(θ)
= 12.0 kg * 9.8 m/s² * cos(30°)
N = Fg_perpendicular
= 12.0 kg * 9.8 m/s² * cos(30°)
Finally, we can calculate the force of static friction:
Ffs = μs * N
= 0.65 * [12.0 kg * 9.8 m/s² * cos(30°)]