Forces - A block slides upward on a rough, vertical wall

In summary, a block of mass 3.0 kg slides upward on a rough, vertical wall at constant velocity with a force F of 60 N acting on it at an angle Ɵ = 60ᵒ to the horizontal. Using Newton's laws, the normal force on the block is found to be -23 N and the force of kinetic friction is determined to be 60cos60° + 23μ = 0. The normal force from the wall is exerted horizontally to the left, while the wall exerts a friction force on the block in the opposite direction of its motion.
  • #1
santoki
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0
forces -- A block slides upward on a rough, vertical wall

Homework Statement



A block slides upward on a rough, vertical wall at constant velocity when a force F of 60 N acts on it at an angle Ɵ = 60ᵒ to the horizontal. The mass of the block is 3.0 kg. See picture below.

dDOgI4J.png


a) Using Newton’s laws, find the normal force on the block.

b) Determine the force of kinetic friction on the block.

2. The attempt at a solution

a) N = mg - Fy = (3.0)(9.8) - 60sin60° = -23

b) Fcos60° - μN = 0
60cos60° + 23μ = 0
μ = -1.3

a negative coefficient?
 
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  • #2
Hello, santoki.

Be sure to draw a good free body diagram. Is the normal force on the block vertical or horizontal?

Note that you are not asked to find the coefficient of friction. You just need to find the force of friction.

Which way does the force of friction act?
 
  • #3
For some reason you assumed the wrong direction for the normal force. Did you draw a free body diagram?
 
  • #4
TSny said:
Hello, santoki.

Be sure to draw a good free body diagram. Is the normal force on the block vertical or horizontal?

Note that you are not asked to find the coefficient of friction. You just need to find the force of friction.

Which way does the force of friction act?

Oh sorry. I drew by FBD like this:

fenr5Jh.jpg
 
  • #5
In the original diagram, the applied force, F, points up and to the right. But in the above drawing, you have it pointing up and to the left.

What surface produces the normal force on the block? Why is it called a "normal" force?
 
  • #6
TSny said:
In the original diagram, the applied force, F, points up and to the right. But in the above drawing, you have it pointing up and to the left.

What surface produces the normal force on the block? Why is it called a "normal" force?

Isn't N the normal force? That's why I drew it pointing to the right because that's the direction the object is exerting force on the wall.
 
  • #7
On the free body diagram of the block, you should only be drawing forces on the block (not on the wall). You are going to apply Newton's laws to the block, so you should be considering the forces on the block.

The normal force that you draw should be the normal force that the wall exerts on the block. What would be the direction of that force? Again, think about the meaning of the word "normal" here.
 
  • #8
TSny said:
On the free body diagram of the block, you should only be drawing forces on the block (not on the wall). You are going to apply Newton's laws to the block, so you should be considering the forces on the block.

The normal force that you draw should be the normal force that the wall exerts on the block. What would be the direction of that force? Again, think about the meaning of the word "normal" here.

So the normal force would be on the right because that's the direction the wall is exerting it's force on the block and the 60N should be on the left because that's the direction it's being exerted on the block? Or would N be pointing to the left horizontally because that's the direction of the force it's exerting on the block?
 
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  • #9
A normal force is a force that is exerted on an object by a surface in a direction that is perpendicular (normal) to the surface.

When you stand on the floor, the floor exerts an upward force on you to support you. In this case the surface of the floor is horizontal while the normal force exerted on you by the floor is vertical (i.e., perpendicular to the floor).

As another example, look at the attached figure which shows a block on an inclined surface. Note how the normal force on the block from the surface is perpendicular to the surface.

In your problem you have a block against a vertical surface (the wall). In what direction does the wall exert a force on the block: upward, downward, to the right, to the left, or none of these?
 

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  • #10
TSny said:
A normal force is a force that is exerted on an object by a surface in a direction that is perpendicular (normal) to the surface.

When you stand on the floor, the floor exerts an upward force on you to support you. In this case the surface of the floor is horizontal while the normal force exerted on you by the floor is vertical (i.e., perpendicular to the floor).

As another example, look at the attached figure which shows a block on an inclined surface. Note how the normal force on the block from the surface is perpendicular to the surface.

In your problem you have a block against a vertical surface (the wall). In what direction does the wall exert a force on the block: upward, downward, to the right, to the left, or none of these?

to the right?
 
  • #11
No. The block pushes on the wall to the right. What does Newton's third law tell you about the force that the wall exerts on the block?
 
  • #12
TSny said:
No. The block pushes on the wall to the right. What does Newton's third law tell you about the force that the wall exerts on the block?

oh okay, I get it. The wall pushes on the block to the left whilst the block pushes on the wall to the right. The third law states they would be exerting the same force in opposite directions.
 
  • #13
Yes, that's right. The normal force on the block from the wall will be horizontal and toward the left.

In addition, the wall exerts a friction force on the block. Can you see what direction the friction force will be on the block? (Remember, the block is sliding upward).
 
  • #14
TSny said:
Yes, that's right. The normal force on the block from the wall will be horizontal and toward the left.

In addition, the wall exerts a friction force on the block. Can you see what direction the friction force will be on the block? (Remember, the block is sliding upward).

Frictional force would be downward in this case. How can I incorporate all of this to finding the normal force and kinetic friction?
 
  • #15
Good. So, now you know that there are 4 forces acting on the block:

(1) Gravity (mg) acting downward
(2) Friction (f) acting downward
(3) Normal (N) acting horizontally to the left
(4) The applied force (F) acing upward and to the right at an angle of 60o above the horizontal.

Draw all of these carefully on a free body diagram. You are given that the block slides with constant velocity. So, think about the acceleration of the block.

What does Newton's 2nd law then tell you about [itex]\sum[/itex]Fx and [itex]\sum[/itex]Fy?
 
  • #16
TSny said:
Good. So, now you know that there are 4 forces acting on the block:

(1) Gravity (mg) acting downward
(2) Friction (f) acting downward
(3) Normal (N) acting horizontally to the left
(4) The applied force (F) acing upward and to the right at an angle of 60o above the horizontal.

Draw all of these carefully on a free body diagram. You are given that the block slides with constant velocity. So, think about the acceleration of the block.

What does Newton's 2nd law then tell you about [itex]\sum[/itex]Fx and [itex]\sum[/itex]Fy?

If it slides with constant velocity, then ay would be 0 so ∑Fy would be 0. And Fx = max, but wouldn't it also equal to 0?
 
  • #17
Yes, good. ∑Fx = 0 and ∑Fy = 0.

Use your free-body diagram to assist with getting the x and y components of the forces.

You should find that ∑Fx = 0 and ∑Fy = 0 will give you two equations you can use to solve for N and f.
(Remember, you do not need to find the coefficient of friction μ, just the force of friction, f.)

Well, I'm off to bed. :zzz: Will check back tomorrow. Good luck.
 
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FAQ: Forces - A block slides upward on a rough, vertical wall

1. What is the force that causes the block to slide upward on the rough, vertical wall?

The force that causes the block to slide upward on the rough, vertical wall is the force of friction. Friction is the force that opposes motion between two surfaces in contact with each other.

2. How does the roughness of the wall affect the block's motion?

The roughness of the wall affects the block's motion by increasing the force of friction between the block and the wall. The rougher the wall, the greater the force of friction, which makes it more difficult for the block to slide upward.

3. Can the block ever slide up the wall without any external force?

No, the block cannot slide up the wall without any external force. In order for the block to move, there needs to be a force acting upon it. In this case, the force of friction between the block and the wall is what allows the block to move upward.

4. What other factors can affect the block's motion on the vertical wall?

Other factors that can affect the block's motion on the vertical wall include the weight of the block, the angle of the wall, and the smoothness of the block's surface. These factors can all impact the force of friction and therefore affect the block's motion.

5. How does the force of gravity play a role in this scenario?

The force of gravity is always acting on the block, pulling it downward toward the ground. However, in this scenario, the force of friction between the block and the wall is strong enough to counteract the force of gravity and allow the block to move upward. Without the force of friction, the block would simply slide down the wall due to the force of gravity.

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