To calculate the coefficient of static friction, we need to use the equation involving the angle of elevation and the coefficient of static friction.
1. Calculate the angle of elevation:
The angle of elevation can be found using the height and length of the board. We can use the inverse tangent function (arctan) to calculate the angle:
angle = arctan(height/length) = arctan(6.0/10.0) ≈ 0.588 radians.
2. With the angle of elevation, we can determine the coefficient of static friction:
The coefficient of static friction, μ (mu), is related to the angle of elevation as follows:
μ = tan(angle) ≈ tan(0.588) ≈ 0.641.
Therefore, the coefficient of static friction is approximately 0.641.
Now, let's move on to the second question.
To calculate the acceleration of the box, we need to consider the forces acting on it. There are two main forces at play: the gravitational force (mg) and the frictional force (static friction in this case).
To determine if we have enough information to calculate the acceleration, let's check what we need:
- Mass of the box (m): This information was not provided in the question.
- The applied force or any other external forces acting on the box: No information about this was given either.
Since we do not have information about the mass of the box or any external forces, we cannot calculate the acceleration at this point. We need either the mass or the net external force acting on the box to proceed with the calculations.
Additional information needed:
- Mass of the box (m).
- Any additional external forces acting on the box.
Once we have this information, we can calculate the acceleration using Newton's second law (F = ma), incorporating the gravitational force and the static friction force.