A block accelerates at 3.3 m/s^2 down a plane inclined at an angle of 26 degrees.Find micro(k) between the block and the inclined plane. The acceleration of gravity is 9.81 m/s^2.
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To find the coefficient of friction (μk) between the block and the inclined plane, we can use the formula:
μk = tan(θ) - a/g
where:
- θ is the angle of inclination
- a is the acceleration of the block down the incline
- g is the acceleration due to gravity
Given:
θ = 26 degrees
a = 3.3 m/s^2
g = 9.81 m/s^2
Plugging in the values:
μk = tan(26) - 3.3 / 9.81
Calculating:
μk = 0.4877
Therefore, the coefficient of friction (μk) between the block and the inclined plane is approximately 0.4877.
To find the coefficient of friction (μk) between the block and the inclined plane, we can use the following steps:
Step 1: Determine the force of gravity acting on the block.
The force of gravity can be calculated using the formula:
Fg = m × g
where m is the mass of the block and g is the acceleration due to gravity (9.81 m/s^2).
Step 2: Resolve the force of gravity into two components.
Since the plane is inclined, we need to split the force of gravity into two components: one parallel to the plane (Fg_parallel) and one perpendicular to the plane (Fg_perpendicular). We can calculate these components as follows:
Fg_parallel = Fg × sin(θ)
Fg_perpendicular = Fg × cos(θ)
where θ is the angle of inclination (26 degrees).
Step 3: Calculate the net force acting on the block.
The net force can be determined by subtracting the force component parallel to the plane from the force necessary to accelerate the block down the plane:
Net force = m × a - Fg_parallel
where a is the acceleration of the block (3.3 m/s^2).
Step 4: Determine the frictional force.
The frictional force (Ffriction) can be calculated as the product of the coefficient of friction (μk) and the normal force (Fn). The normal force can be calculated as the force component perpendicular to the plane (Fg_perpendicular). Thus, we have:
Ffriction = μk × Fn
Step 5: Equate the net force and frictional force.
Since the net force and frictional force should be equal (as the block is in equilibrium), we can set them equal to each other:
Net force = Ffriction
Step 6: Solve for the coefficient of friction.
Substituting the values we found in the previous steps, we can solve for μk:
m × a - Fg_parallel = μk × Fg_perpendicular
μk = (m × a - Fg_parallel) / Fg_perpendicular
By plugging in the given values for mass, acceleration, angle of inclination, and acceleration due to gravity, you can calculate the coefficient of friction (μk) between the block and the inclined plane.