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?
force down = 2.27* 9.81
.79* F = 2.27*9.81
F = 28.2 N
To determine the minimum amount of pressing force required to keep the picture properly positioned against the wall, we need to consider the forces acting on the picture.
The force of gravity, denoted as Fg, is given by the equation:
Fg = m * g
where m is the mass of the picture and g is the acceleration due to gravity. In this case, m = 2.27 kg and g is approximately 9.8 m/s^2.
Fg = 2.27 kg * 9.8 m/s^2
Fg = 22.246 N
The force of static friction, denoted as Fs, is given by the equation:
Fs = μ * N
where μ is the coefficient of static friction and N is the normal force. In this case, the normal force is equal to the force of gravity, as the picture is pressed against the wall perpendicular to the surface.
N = Fg = 22.246 N
Substituting the values for the coefficient of static friction and the normal force:
Fs = 0.790 * 22.246 N
Fs = 17.54354 N (approximately)
Therefore, the minimum amount of pressing force that must be used to keep the picture properly positioned against the wall is approximately 17.54354 N.
To determine the minimum amount of pressing force needed, we need to consider the equilibrium condition for the picture on the wall. In this case, the maximum frictional force between the picture and the wall will oppose the pressing force and keep the picture from sliding down.
The maximum frictional force (Ff) can be calculated using the formula:
Ff = μ * N
where μ is the coefficient of static friction and N is the normal force exerted by the picture on the wall. The normal force is equal to the weight of the picture, which can be calculated using the formula:
N = m * g
where m is the mass of the picture and g is the acceleration due to gravity (9.8 m/s^2).
Therefore, the maximum frictional force can be found by substituting the values into the equation:
Ff = 0.790 * (2.27 kg * 9.8 m/s^2)
Now, we have the maximum frictional force. To find the minimum amount of pressing force needed, we just need to set the pressing force equal to the maximum frictional force, since they will be equal in order to maintain equilibrium:
Pressing force = Maximum frictional force
So, the minimum amount of pressing force needed to properly position the picture against the wall is equal to the maximum frictional force calculated above.