A 248-kg crate rests on a surface that is inclined above the horizontal at an angle of 19.5°. A horizontal force (magnitude = 537 N and parallel to the ground, not the incline) is required to start the crate moving down the incline. What is the coefficient of static friction between the crate and the incline?
can some1 plz explain this to me?
To start the crate sliding down the incline, you must provide a force component in that direction that exceeds the maximum static friction force minus the weight component in that direction.
When the two forces are equal,
M g cos 19.5 * Us = M g sin 19.5 + 537 cos19.5
where Us is the static friction coefficient.
Solve for Us
could you clarify what M is? i know g is the gravity which will be 9.81 but im not sure about the M
To find the coefficient of static friction between the crate and the incline, we need to understand the forces acting on the crate and the conditions required for it to start moving.
Here's how you can solve it step by step:
Step 1: Identify the known values from the problem.
- Mass of the crate (m) = 248 kg
- Angle of the incline (θ) = 19.5°
- Applied horizontal force (F_applied) = 537 N
Step 2: Determine the gravitational force acting on the crate.
The force of gravity acting on the crate can be calculated using the formula:
Gravitational force (F_gravity) = mass (m) * acceleration due to gravity (g)
where the acceleration due to gravity (g) is approximately 9.8 m/s^2.
Substituting the given values:
F_gravity = 248 kg * 9.8 m/s^2
Step 3: Find the component of the gravitational force acting parallel to the incline.
The component of the gravitational force acting parallel to the incline can be found using the formula:
Force parallel to incline (F_parallel) = F_gravity * sin(θ)
where θ is the angle of the incline.
Substituting the known values:
F_parallel = F_gravity * sin(19.5°)
Step 4: Determine the force of static friction.
Since the crate is initially at rest, the force of static friction opposes the applied force. Therefore, the force of static friction is equal to the applied force required to start the motion of the crate.
Force of static friction (F_friction) = F_applied
Step 5: Calculate the coefficient of static friction.
The coefficient of static friction (μ_static) can be calculated using the formula:
μ_static = F_friction / F_normal
where F_normal is the normal force acting on the crate, which is equal to the component of gravitational force acting perpendicular to the incline.
F_normal = F_gravity * cos(θ)
Substituting the known values for F_gravity, F_parallel, and F_normal, we can calculate the coefficient of static friction (μ_static).
I hope this explanation helps you understand how to solve this problem.