A person is trying to judge whether a picture (mass = 2.37 kg) is properly positioned by temporarily pressing it against a wall. The pressing force is perpendicular to the wall. The coefficient of static friction between the picture and the wall is 0.760. What is the minimum amount of pressing force that must be used?
To determine the minimum amount of pressing force required for the picture to remain in place against the wall, we can use the following steps:
Step 1: Identify the relevant equations:
The equation that relates the force of static friction to the normal force and the coefficient of static friction is:
Fs = μs * N
Where:
Fs is the force of static friction,
μs is the coefficient of static friction,
N is the normal force.
Step 2: Identify the forces acting on the picture:
In this case, the only vertical force acting on the picture is its weight, which is given as the mass (m = 2.37 kg) times the acceleration due to gravity (g = 9.8 m/s^2).
Therefore, the weight acting on the picture is:
W = m * g
Step 3: Calculate the normal force:
The normal force is equal in magnitude but opposite in direction to the weight of the picture. Therefore, the normal force can be calculated as:
N = -W
Step 4: Calculate the minimum amount of pressing force:
To calculate the minimum amount of pressing force, we substitute the known values into the equation for static friction:
Fs = μs * N
Substituting N = -W, we have:
Fs = μs * (-W)
Considering that the pressing force is equal in magnitude but opposite in direction to the force of static friction, we have:
|Fp| = |Fs| = μs * |W|
Therefore, the minimum amount of pressing force required is:
|Fp| = μs * |W|
Step 5: Calculate the minimum amount of pressing force:
Substituting the given values, we can calculate the minimum amount of pressing force:
|Fp| = 0.760 * (2.37 kg * 9.8 m/s^2)
|Fp| ≈ 17.81 N
Therefore, the minimum amount of pressing force that must be used is approximately 17.81 N.
To find the minimum amount of pressing force required to determine if the picture is properly positioned against the wall, we need to consider the maximum force of static friction.
The formula for static friction is given by:
f_s = μ_s * N
where:
f_s is the force of static friction,
μ_s is the coefficient of static friction, and
N is the normal force.
In this case, the normal force N on the picture is equal to its weight, since it is pressed against the wall perpendicular to the surface. The weight W is given by:
W = m * g
where:
m is the mass of the picture, and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the values, we have:
W = 2.37 kg * 9.8 m/s^2
Next, we can calculate the maximum force of static friction by multiplying the coefficient of static friction (μ_s) by the normal force (N):
f_s = μ_s * N
Substituting the calculated weight for the normal force, we have:
f_s = 0.760 * (2.37 kg * 9.8 m/s^2)
Finally, we can determine the minimum amount of pressing force required by considering that the pressing force must be equal to or greater than the maximum force of static friction to avoid any sliding:
Minimum pressing force = f_s
Now, you can calculate the minimum pressing force by plugging in the values into the equation and solving for f_s.