Minimum force to make box slide down slope

In summary, the minimum force needed to make the box slide down the slope with a mass of 5.0kg and an angle of 30 degrees is 12N. This is calculated by taking into account the force of static friction, the normal force, and the force of gravity.
  • #1
heartshapedbox
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Homework Statement



If m=5.0kg, φ=30◦ and μs =0.87, what is the minimum force needed to make the box slide down the slope?

[/B]

Homework Equations


force of status friction is less than or equal to the normal force multiplied by the coefficient of static friction
F,normal=mgcosφ

The image is a slope of angle 30 degrees with box, mass 5kg on it. The force is being applied so that the box will slide downward when enough force is applied.

The Attempt at a Solution



Because the F of static friction is equal to coefficient of static friction multiplied by the normal force I got;

F,sf=((9.8)(5)cos(30))(0.87)=36.9N Therefore, the force would have to be greater than this, say 37N

The correct answer is apparently 12N I do not know why! [/B]
 
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  • #2
Hint: Is friction the only force acting on the box?
 
  • #3
Thank you! x

Fn=|Fn|cosθ k`
Fg= -mg k`
Ff= |Fn|(us) i`
Fpush=Ff-mgsinθ

Therfore,

us(mgcosθ)-mgsinθ

(0.87(5x9.8(cos30)))-5x9.8xsin30
=12N

yes? ahaha :p
 

FAQ: Minimum force to make box slide down slope

What is the minimum force needed to make a box slide down a slope?

The minimum force needed to make a box slide down a slope depends on several factors such as the weight of the box, the angle of the slope, and the coefficient of friction between the box and the slope. It can be calculated using the formula F=μmgcosθ, where F is the minimum force, μ is the coefficient of friction, m is the mass of the box, g is the acceleration due to gravity, and θ is the angle of the slope.

How does the angle of the slope affect the minimum force needed?

The angle of the slope has a direct impact on the minimum force needed to make a box slide down. As the angle of the slope increases, the minimum force required also increases. This is because the steeper the slope, the greater the force needed to overcome the force of gravity pulling the box down the slope.

What is the significance of the coefficient of friction in determining the minimum force?

The coefficient of friction is a measure of how much resistance there is between two surfaces in contact. In the case of a box sliding down a slope, the coefficient of friction between the box and the slope determines how much force is needed to overcome the friction and make the box slide down. A higher coefficient of friction means a greater force is needed to make the box slide.

Can the minimum force vary for different types of boxes?

Yes, the minimum force needed to make a box slide down a slope can vary depending on the weight and surface of the box. A heavier box will require more force to overcome the force of gravity, while a box with a smoother surface may have a lower coefficient of friction and therefore require less force to slide down a slope.

Is the minimum force the same as the force needed to keep the box sliding down the slope?

No, the minimum force needed is the initial force required to make the box start sliding down the slope. Once the box is in motion, the force needed to keep it sliding will depend on other factors such as air resistance and the surface of the slope. In most cases, the force needed to keep the box sliding will be less than the minimum force needed to start it sliding.

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