Finding the minimum force F which must be exerted

In summary: Your FBDs do not agree with each other. For example, the Fn you show on the 6 kg block is upward and to the left; the Fn you show on the wedge is straight up. There should be one Fn that is the opposite of the other. You also have not distinguished the fact that there are two normal forces involved. And it goes on...
  • #1
rando25
3
0

Homework Statement


Given: The friction between the block with mass 6 kg and the wedge with mass 18 kg is 0.27 . The surface between the wedge with mass 18 kg and the horizontal plane is smooth (without friction). The acceleration of gravity is 9.8 m/s^ 2. A block is released on the inclined plane (top side of the wedge). What is the minimum force F which must be exerted on the 18 kg block in order that the 6 kg block does not move down the plane?
29zen9h.jpg


Homework Equations


Fnet = ma
and possibly(?): Ff = uFn

The Attempt at a Solution


Having the wedge in the problem is confusing me.
The forces acting on the x-axis of the 18 kg block are F applied and Fg parallel
The forces acting on the x-axis of the 6kg block are F frictional and Fg parallel.
Fnet = ma / Fnet = 0
Fa + Fg(parallel) = 0
I think I am solving for Fa (18kg), I'm not sure.
Fa = Fgsin20
Fa = (18kg)(9.8m/s2)sin20
Fa = 60.33 N
I know the 6kg block plays a role, but i don't know how or where to incorporate it.
I'm really confused, any help is appreciated.
 
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  • #2
Having the wedge in the problem is designed to get you to think.

Start with FBDs for both the wedge and the 6 kg block and write equations of motion for each AFTER you draw the FBDs.
 
  • #3
OldEngr63 said:
Having the wedge in the problem is designed to get you to think.

Start with FBDs for both the wedge and the 6 kg block and write equations of motion for each AFTER you draw the FBDs.
 
  • #4
OldEngr63 said:
Having the wedge in the problem is designed to get you to think.

Start with FBDs for both the wedge and the 6 kg block and write equations of motion for each AFTER you draw the FBDs.
upload_2014-11-28_18-22-38.png

this is my work so far. I know I am looking of F at this point, but I am still not sure where to go from here? (unless my FBDs are incorrect...)
 
  • #5
Your FBDs do not agree with each other. For example, the Fn you show on the 6 kg block is upward and to the left; the Fn you show on the wedge is straight up. There should be one Fn that is the opposite of the other. You also have not distinguished the fact that there are two normal forces involved. And it goes on...

I suggest that you try again on the FBDs.
 

FAQ: Finding the minimum force F which must be exerted

What is the definition of minimum force?

Minimum force is the smallest amount of force that is required to achieve a certain outcome or result.

Why is it important to find the minimum force?

Finding the minimum force is important because it allows us to understand the minimum amount of energy or effort that is needed to produce a desired effect. This can help us optimize processes and reduce waste.

How do you calculate the minimum force?

The minimum force can be calculated using the equation F = ma, where F is the force, m is the mass of the object, and a is the acceleration. This equation is derived from Newton's second law of motion.

What factors affect the minimum force?

The minimum force can be affected by various factors such as the mass and shape of the object, friction, and external forces acting on the object. These factors can either increase or decrease the minimum force required.

Can the minimum force change?

Yes, the minimum force can change depending on the factors mentioned above. For example, if the mass of the object increases, the minimum force required to move it will also increase. Similarly, if external forces are applied, the minimum force needed to counteract them will also change.

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