A person is trying to judge whether a picture (mass = 2.27 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 0.790. What is the minimum amount of pressing force that must be used?
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To find the minimum amount of pressing force that must be used, we first need to understand the concept of static friction.
Static friction is the force that acts between two surfaces in contact with each other, and it prevents an object from moving when there is an attempt to move it. The magnitude of static friction depends on the coefficient of static friction (μ) and the normal force (N) between the two surfaces.
In this case, the normal force is equal to the weight of the picture, which is the product of its mass (m) and the acceleration due to gravity (g). We can calculate the normal force using the formula:
N = m * g
Next, we can calculate the maximum static friction force by multiplying the coefficient of static friction (μ) by the normal force (N):
f_static_max = μ * N
Finally, the minimum amount of pressing force required will be equal to the maximum static friction force:
Minimum Pressing Force = f_static_max
Let's plug in the given values into the formulas and calculate the result.
Given:
Mass of the picture (m) = 2.27 kg
Coefficient of static friction (μ) = 0.790
Acceleration due to gravity (g) = 9.8 m/s^2 (approximate value)
Step 1: Calculate the normal force (N)
N = m * g
N = 2.27 kg * 9.8 m/s^2
N ≈ 22.246 N
Step 2: Calculate the maximum static friction force (f_static_max)
f_static_max = μ * N
f_static_max = 0.790 * 22.246 N
f_static_max ≈ 17.575 N
Therefore, the minimum amount of pressing force that must be used is approximately 17.575 Newtons.