A 2.0kg siverware drawer become stuck, so the owner graually pulls with more and more force. When the applied force reaches 8.0N the drawer suddenly opens, throwing the utensils to the floor. Find the Coefficient fo static friction between the drawer and the cabinet?
Static friction force = 8.0 N =
(static friction coefficient) x M g
M = 2.0 kg; g = 9.8 m/s^2
Solve for the static friction coefficient
What is the equation with out the Numbers
is it Sum of the Forces=mg
To find the coefficient of static friction between the drawer and the cabinet, we can use Newton's second law of motion and the equation for static friction.
Step 1: Determine the mass of the drawer.
Given that the drawer has a mass of 2.0 kg.
Step 2: Determine the force required to open the drawer.
The force required to open the drawer is the maximum force applied before it opens, which is 8.0 N.
Step 3: Write the equation for static friction.
According to Newton's second law of motion, the force required to overcome static friction (F_friction) is equal to the product of the coefficient of static friction (μ_s) and the normal force (N):
F_friction = μ_s * N
Step 4: Calculate the normal force.
The normal force (N) is the force exerted by a surface to support the weight of an object resting on it. In this case, it is equal to the weight of the drawer, which is given by:
N = m * g
where m is the mass of the drawer and g is the acceleration due to gravity (9.8 m/s^2).
Step 5: Substitute the values into the equation for static friction.
F_friction = μ_s * N
8.0 N = μ_s * (2.0 kg * 9.8 m/s^2)
Solving for μ_s:
μ_s = 8.0 N / (2.0 kg * 9.8 m/s^2)
Step 6: Calculate the coefficient of static friction.
μ_s = 8.0 N / (2.0 kg * 9.8 m/s^2)
μ_s = 0.408
Therefore, the coefficient of static friction between the drawer and the cabinet is 0.408.