Block Pushed Up a Vertical Wall

[AngeliaGW]

Homework Statement

What force is needed to move a 10 pound block up a vertical wall at a constant speed by pushing at an angle of 53 degrees with the vertical? Mu=0.3

At what minimum angle with the vertical would you be unable to push the block at all regardless of how large the force is?

Homework Equations

Y: Fcos53-weight-(Mu*NormalForce) = 0
NormalForce-Fsin53=0

The Attempt at a Solution

I solved the force needed to push the block up a constant wall which is 27.6 lbs. However, I'm unsure of the second part of the question.

 

[NascentOxygen]

The normal component of the applied force produces a frictional force. So you have a number of forces acting parallel to the wall. To cause movement upwards, the parallel components acting in the UP direction must be greater in magnitude than those acting DOWN.

 

[AngeliaGW]

Yes but how would I find the angle where no matter what force is applied in the parallel components acting up, the block wouldn't move?

 

[NascentOxygen]

The second part is more interesting than I at first thought!

As you found, the condition for movement up the wall is that F.cosA > u.F.sinA + m.g

Re-arrange to get F on one side of the inequality by itself. Then, for a given angle, A, you can calculate the value of F needed to cause movement. You will find that as the angle nears some particular value, the necessary force grows rapidly, until at some angle the force to cause movement becomes infinite. I think you will see the relationship in that equation.

 

[AngeliaGW]

I'm unsure as to how you got that inequality. Does u. mean Mu? A hint that was given to solve this problem was that sin^2Theta + cos^2Theta = 1.

 

[NascentOxygen]

Yes, I use 'u' to represent mu as my browser won't accept greek letters. By the same token, I used A whereas a theta would be preferable.

That hint doesn't help me.

 

[AngeliaGW]

I derived the equation F(CosTheta-.3SinTheta) > 10. With 2 variables (F and theta), how would this equation be solved to find the angle?

 

[NascentOxygen]

I derived the equation F(CosTheta-.3SinTheta) > 10. With 2 variables (F and theta), how would this equation be solved to find the angle?

That 10 isn't right.

You don't solve it. There are two variables and only one equation. I suggest that you follow the procedure I suggested, viz.,

Re-arrange to get F on one side of the inequality by itself. Then, for a given angle, theta, you can calculate the value of F needed to cause movement. You will find that as the angle nears some particular value, the necessary force grows rapidly, until at some angle the force to cause movement becomes infinite. I think you will see the relationship in that equation.

You choose some value of Theta, and determine F. Choose a larger value for Theta, and determine F now. And so on, until you see some relationship.