If the coefficient of static friction between the board and the wall is 0.81, what is the least force you can apply and still hold the board in place?
if board mass = m
down force = m g
so friction force must be m g
mu F = m g
F = m g/mu
To find the least force you can apply and still hold the board in place, you need to use the formula that relates the force of static friction (F_f) to the coefficient of static friction (μ) and the normal force (F_N).
The formula is: F_f = μ * F_N
In this case, the normal force is the force perpendicular to the surface, which is equal to the weight of the board in this scenario.
To find the normal force, you need to know the weight of the board. Let's say the weight of the board is W.
Now, to find the least force you can apply and hold the board in place, you need to calculate F_f.
F_f = μ * F_N
F_f = μ * W
Given that the coefficient of static friction (μ) is 0.81, and the weight of the board is W, you can use these values to calculate F_f.
To determine the least force required to hold the board in place, you need to consider the concept of static friction. Static friction is the force that prevents two objects from sliding when they are in contact and at rest.
The equation for static friction is given by:
fs ≤ μs * N
Where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force. The normal force is the force exerted by a surface perpendicular to the contact surface.
In this case, the board is leaned against the wall, so the normal force is equal to the weight of the board, which can be calculated using the formula:
N = m * g
Where m is the mass of the board and g is the acceleration due to gravity.
By combining these formulas, we can determine the least force required to hold the board in place:
fs ≤ μs * N
fs ≤ μs * (m * g)
Substituting the given coefficient of static friction (0.81) into the equation, we get:
fs ≤ 0.81 * (m * g)
To find the least force, we need to determine the maximum value of fs. This occurs when the board is just about to start moving, which is when the force of static friction is at its maximum. Therefore, the least force required to hold the board in place is equal to the force of static friction:
fs = μs * (m * g)
Now, you can calculate the least force required by knowing the mass of the board and the acceleration due to gravity, and substituting them into the equation above.