A 4.0-kg block is at rest on a horizontal floor. If you push horizontally on the 4.0-kg block with a force of 12.0 N, it just starts to move. What is the coefficient of static friction?
12N=mg*mu
solve for mu.
what is mg?
To determine the coefficient of static friction, we can use the formula:
Fs = μs * N
where Fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
Since the block is at rest on the floor, the force of static friction exactly cancels out the applied force. Therefore, we can equate the force of static friction with the applied force:
Fs = F_applied
Substituting the values given:
Fs = 12.0 N
We need to find the normal force, which is equal to the weight of the block. The weight can be calculated using the formula:
Weight = mass * acceleration due to gravity
Weight = 4.0 kg * 9.8 m/s^2
Weight = 39.2 N
Now, we can find the coefficient of static friction by rearranging the equation:
μs = Fs / N
μs = 12.0 N / 39.2 N
μs ≈ 0.306
Therefore, the coefficient of static friction is approximately 0.306.
To determine the coefficient of static friction, we can use the equation:
F_applied = μ_s * N
where:
F_applied is the applied force,
μ_s is the coefficient of static friction, and
N is the normal force.
In this case, we are given that the applied force is 12.0 N and the mass of the block is 4.0 kg. We need to find the coefficient of static friction.
When the block is at rest, the force of static friction exactly balances the applied force, preventing the block from moving. This means that the force of static friction is equal in magnitude and opposite in direction to the applied force.
Therefore, the force of static friction is also 12.0 N.
To find the normal force, we can use the equation:
N = m * g
where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the given values, we get:
N = 4.0 kg * 9.8 m/s^2 = 39.2 N
Now, we can substitute the known values for the force of static friction (12.0 N) and the normal force (39.2 N) into the equation:
12.0 N = μ_s * 39.2 N
Simplifying the equation:
μ_s = 12.0 N / 39.2 N ≈ 0.31
Therefore, the coefficient of static friction (μ_s) is approximately 0.31.