Solving Physics Questions: Minimum Force and Friction Coefficient

[physicshelpme]

!Physics Questions! Help!

An artist must push with a minimum force of 75 N at an angle of 45° to a picture to hold it in equilibrium. The coefficient of friction between the wall and the picture frame is 0.30.
What is the mass of the picture?

 

[quantumdude]

Originally posted by physicshelpme
An artist must push with a minimum force of 75 N at an angle of 45° to a picture to hold it in equilibrium. The coefficient of friction between the wall and the picture frame is 0.30.
What is the mass of the picture?

Hi, and welcome to PF. Here in the Homework Help forum, I ask that you show how you started, and where you got stuck (see the thread "Read This Before Posting" at the top of the forum).

As with all problems in statics, you have to...

1. Draw the free body diagram.
2. Set up Newton's 2^nd law for the problem.
3. Solve the equation(s).

Try that, post your work, and indicate where you got stuck. We'll help you through the rough spots.

 

[M98Ranger]

To solve this physics question, we can use the equation for equilibrium: ΣF = 0, where ΣF is the sum of all forces acting on the picture. In this case, the only forces acting on the picture are the artist's push and friction from the wall.

First, we need to find the horizontal and vertical components of the artist's push. The horizontal component can be found using the cosine function: Fx = Fcosθ = 75 Ncos45° = 53.03 N. The vertical component can be found using the sine function: Fy = Fsinθ = 75 Nsin45° = 53.03 N.

Next, we can use the equation for friction: Ff = μN, where Ff is the force of friction, μ is the coefficient of friction, and N is the normal force. The normal force is equal to the weight of the picture, which we can find using the equation Fg = mg, where Fg is the weight, m is the mass, and g is the acceleration due to gravity (9.8 m/s²). So, N = mg = 9.8m. Substituting this into the equation for friction, we get Ff = 0.30(9.8m) = 2.94m.

Now, we can set up an equation for the horizontal forces in the x-direction: ΣFx = Fx - Ff = 53.03 N - 2.94m = 0. Since the picture is in equilibrium, the sum of the forces in the x-direction must be equal to 0. Solving for m, we get m = 53.03 N / 2.94 = 18.03 kg.

Therefore, the mass of the picture is approximately 18.03 kg.