A 1,440-N crate is being pushed across a level floor at a constant speed by a force of 210 N at an angle of 20.0° below the horizontal, as shown in the figure (a) below
(a) What is the coefficient of kinetic friction between the crate and the floor
137.1
it says i'm within 10 percent but there might be a round off error.
To find the coefficient of kinetic friction between the crate and the floor, we need to analyze the forces acting on the crate.
1. Identify the forces acting on the crate:
- Applied force: F_applied = 210 N at an angle of 20.0° below the horizontal.
- Weight (force due to gravity): F_weight = mass * gravity (since the crate is on a level floor, its weight acts vertically downward).
2. Find the weight of the crate:
The weight of an object can be calculated using the formula F_weight = mass * gravity.
Since the weight force and the normal force are equal and opposite, the normal force will have the same magnitude and point vertically upward.
3. Calculate the normal force:
The normal force, denoted as F_normal, can be found by using the equation F_normal = F_weight = mass * gravity.
4. Determine the frictional force:
The frictional force can be calculated using the equation F_friction = μ * F_normal, where μ is the coefficient of kinetic friction. Here, the crate is moving at a constant speed, so we are dealing with kinetic friction.
5. Find the coefficient of kinetic friction:
Rearrange the equation F_friction = μ * F_normal to solve for μ:
μ = F_friction / F_normal.
It is important to note that we do not have the mass of the crate given in the question. However, we can use the weight F_weight instead, as weight is directly proportional to mass.
Therefore, the coefficient of kinetic friction can be calculated as follows:
μ = F_friction / F_normal
= (F_applied - F_weight) / F_normal
= (F_applied - (mass * gravity)) / (mass * gravity)