A 3.0-kg block is at rest on a horizontal floor. If you push horizontally on the 3.0-kg block with a force of 12.0N it just starts to move. What is the coefficient of static friction?
net force= m*a
12-friction= mass*0
but friction = mu*mg
solve for mu.
To find the coefficient of static friction, we can use the equation:
\(F_{\text{friction}} = \mu_s \cdot F_{\text{normal}}\)
Where:
\(F_{\text{friction}}\) is the force of friction,
\(\mu_s\) is the coefficient of static friction, and
\(F_{\text{normal}}\) is the normal force.
In this case, the force of friction is equal to the applied force (12.0N) because the block just starts to move. The normal force is equal to the weight of the block (mg), where \(m\) is the mass of the block and \(g\) is the acceleration due to gravity (9.8 m/s²).
Given that the mass of the block is 3.0 kg, we can calculate the normal force:
\(F_{\text{normal}} = m \cdot g\)
\(F_{\text{normal}} = 3.0 \, \text{kg} \cdot 9.8 \, \text{m/s²}\)
\(F_{\text{normal}} = 29.4 \, \text{N}\)
Now, we can substitute the values into the equation and solve for the coefficient of static friction:
12.0N = \(\mu_s \cdot\) 29.4N
Rearranging the equation, we get:
\(\mu_s = \frac{12.0 \, \text{N}}{29.4 \, \text{N}}\)
Evaluating this expression, we find:
\(\mu_s \approx 0.408\)
Therefore, the coefficient of static friction is approximately 0.408.
To find the coefficient of static friction, we need to use the equation for static friction:
fs = μs * N
where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
In this case, the normal force N is equal to the weight of the block, which can be calculated using 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/s²).
Given that the mass of the block is 3.0 kg, the weight can be calculated as:
N = 3.0 kg * 9.8 m/s² = 29.4 N
Now, we know that the block just begins to move when a horizontal force of 12.0 N is applied. This force is equivalent to the force of static friction fs acting in the opposite direction:
fs = 12.0 N
Substituting the known values into the equation for static friction:
12.0 N = μs * 29.4 N
Solving for μs:
μs = 12.0 N / 29.4 N ≈ 0.408
Therefore, the coefficient of static friction (μs) is approximately 0.408.