A box has mass 13 kg and is at rest on a flat floor. A minimum force of 47 N is needed to push the box so it moves across the floor. What is the coefficient of static friction between the box and floor?
M*g = 13 * 9.8 = 127.4 N. = Wt. of box =
Normal force(Fn).
Fap-Fs = M*a
47 - Fs = M*0 = 0
Fs = 47 N. = Force of static friction.
us = Fs/Fn = 47/127.4 = 0.369
To find the coefficient of static friction between the box and the floor, we can use the equation:
\[ \text{Force of friction} = \text{coefficient of friction} \times \text{normal force} \]
In this case, the force of friction acting on the box is the minimum force needed to push it, which is 47 N. The normal force between the box and the floor is equal to the weight of the box, which can be calculated by multiplying the mass of the box (13 kg) by the acceleration due to gravity (9.8 m/s^2).
Let's calculate the normal force first:
\[ \text{Normal force} = \text{mass} \times \text{acceleration due to gravity} = 13 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]
Now we can substitute the values into the equation to find the coefficient of static friction:
\[ 47 \, \text{N} = \text{coefficient of static friction} \times (\text{mass} \times \text{acceleration due to gravity}) \]
We can rearrange the equation to solve for the coefficient of static friction:
\[ \text{coefficient of static friction} = \frac{47}{(\text{mass} \times \text{acceleration due to gravity})} \]
Let's calculate the coefficient of static friction:
\[ \text{coefficient of static friction} = \frac{47}{(13 \, \text{kg} \times 9.8 \, \text{m/s}^2)} \]
\[ \text{coefficient of static friction} \approx 0.363 \]
Therefore, the coefficient of static friction between the box and the floor is approximately 0.363.