Static Friction of sliding box on plane

In summary, the problem involves calculating the applied force (F) using the formula Fs = μ FN, with FN being the normal force between the boxes. The calculated normal force is 64.8N, but the desired force is 46N. After realizing the mistake, the correct acceleration of the small box is calculated to be 13.8 m/s^2 and the applied force is determined to be 465N.
  • #1
goonking
434
3

Homework Statement


BaQTzvR.png


Homework Equations


Fs = μ FN

The Attempt at a Solution


Ok, so I drew a free body diagram and tilted it 90 degrees so that Fg of the small box points right and Fstatic points left.

Fg = 4.7 kg x 9.8m/s2 = 46 N

we want Fs to equal 46 N , correct? so we use the formula

Fs = (0.71) x FN

FN being the force of big box on small box

.71 x FN = 46 N

FN = 64.8N

Which is wrong. any help?
 
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  • #2
goonking said:

Homework Statement


BaQTzvR.png


Homework Equations


Fs = μ FN

The Attempt at a Solution


Ok, so I drew a free body diagram and tilted it 90 degrees so that Fg of the small box points right and Fstatic points left.

Fg = 4.7 kg x 9.8m/s2 = 46 N

we want Fs to equal 46 N , correct? so we use the formula

Fs = (0.71) x FN

FN being the force of big box on small box

.71 x FN = 46 N

FN = 64.8N

Which is wrong. any help?

You calculated the normal force between the boxes, but you need the applied force, F.
 
  • #3
What is the required acceleration of box one? How is the mass of box one relevant?
 
  • #4
ehild said:
You calculated the normal force between the boxes, but you need the applied force, F.
oh, silly me.

so the acceleration of the small box should be 64.8 / 4.7k which is 13.8 m/s^2

we use F=ma , m being mass of both boxes together and a being 13.8 m/s^2

F = 465 N
 
  • #5
goonking said:
so the acceleration of the small box should be 64.8 / 4.7k which is 13.8 m/s^2

we use F=ma , m being mass of both boxes together and a being 13.8 m/s^2

F = 465 N
Correct!
 

FAQ: Static Friction of sliding box on plane

What is static friction and how does it affect a sliding box on a plane?

Static friction is a force that prevents two surfaces from sliding past each other when they are in contact and not moving relative to each other. In the case of a sliding box on a plane, static friction acts in the opposite direction of the applied force, preventing the box from sliding down the plane.

How is the coefficient of static friction determined for a box on a plane?

The coefficient of static friction is determined by dividing the maximum amount of static friction by the applied force. This value is dependent on the materials of the surfaces in contact and the roughness of those surfaces.

What factors can affect the static friction of a sliding box on a plane?

The static friction of a sliding box on a plane can be affected by the weight of the box, the angle of the plane, the coefficient of static friction between the surfaces, and the roughness of the surfaces in contact.

How does the angle of the plane affect the static friction of a sliding box?

The angle of the plane affects the component of the weight of the box that acts in the direction of the plane, which in turn affects the maximum amount of static friction that can be exerted on the box. As the angle of the plane increases, the component of the weight acting in the direction of the plane decreases, resulting in a decrease in the maximum static friction.

What is the difference between static friction and kinetic friction in the context of a sliding box on a plane?

Static friction prevents two surfaces from sliding past each other when they are not moving relative to each other, while kinetic friction acts on two surfaces that are moving relative to each other. In the case of a sliding box on a plane, static friction is present when the box is not moving, but once it starts moving, the force of kinetic friction takes over.

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