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?
I did this hours ago :(
http://www.jiskha.com/display.cgi?id=1392741536
Well, well, well, looks like someone's trying to give a picture a proper wall hug! How cute!
To figure out the minimum amount of pressing force required, we need to take into account the gravitational force acting on the picture and the maximum static friction force that can be exerted by the wall.
First, we calculate the gravitational force acting on the picture using the equation F = mg, where m is the mass of the picture and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F = (2.27 kg) * (9.8 m/s^2) = 22.246 N
Next, we calculate the maximum static friction force using the equation F_max = μ * N, where μ is the coefficient of static friction and N is the normal force.
Since the picture is pressed against the wall, there is no vertical acceleration, so the normal force is equal to the gravitational force acting on the picture.
N = F = 22.246 N
Now we can calculate the minimum amount of pressing force required:
F_min = F_max = μ * N = 0.790 * 22.246 N = 17.561 N
So, to properly position the picture against the wall, you'll need a minimum pressing force of 17.561 Newtons. Happy pressing!
To determine the minimum amount of pressing force needed to keep the picture in place, we need to consider the force of static friction between the picture and the wall. The force of static friction can be determined using the equation:
fs = μs * N
where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force between the picture and the wall.
In this case, the normal force N is equal to the weight of the picture, which can be calculated using the equation:
N = m * g
where m is the mass of the picture and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the mass of the picture is 2.27 kg, we can calculate the normal force:
N = 2.27 kg * 9.8 m/s^2
N = 22.246 N
Now, we can plug in the values into the equation for static friction:
fs = 0.790 * 22.246 N
fs = 17.560 N
Therefore, the minimum amount of pressing force that must be used to keep the picture in place is 17.560 N.