Calculating the Angle of Static Friction for a Crane Lifting a Box

In summary, the small crane is lifting a 10kg box of nails and if the coefficient of static friction is .4, then the angle at which the box begins to slide would be the inverse of tan multiplied by .4.
  • #1
Nicolaus
73
0

Homework Statement


A small crane is lifting a 10kg box of nails. If the coefficient of static friction is .4, calculate the angle at which the box begins to slide.


Homework Equations


Fg x component: mg sin
Ff = ukmgcos


The Attempt at a Solution


Fnet = Fgx - Ff
Would the net force be zero since there's no acceleration in its static state?
Do I then rearrange the equation to solve for the angle?
 
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  • #2
Hi Nicolaus! :wink:
Nicolaus said:
Would the net force be zero since there's no acceleration in its static state?
Do I then rearrange the equation to solve for the angle?

(I don't understand the actual question, but …)

That's correct: for static friction, the acceleration is zero, and so the net force is zero.

And yes, rearrange and solve for the angle :smile:
 
  • #3
Ok, would it then make sense that the result ends up being just the inverse of tan multiplied by 0.4 (which is the coefficient of the static friction): angle = tan(inverse) x .4
 
  • #4
erm :redface:

i've already said i don't understand the question :confused:
 
  • #5
Is it the way it was worded or..? Imagine the box was on a flat board and you slowly start to tilt the board.

EDIT: I think I did this wrong. I'm supposed to calculate the Force of static friction on the flat surface to find the minimum force required for it to move then place that value into the equation (ignoring the cos angle).
Can someone correct me on this.
 
Last edited:
  • #6
Nicolaus said:
A small crane is lifting a 10kg box of nails. If the coefficient of static friction is .4, calculate the angle at which the box begins to slide.
Nicolaus said:
Is it the way it was worded or..? Imagine the box was on a flat board and you slowly start to tilt the board.

ah, in that case, the crane isn't lifting the box, it's lifting the board :wink:

and yes, tan-1µk would be correct :smile:
EDIT: I think I did this wrong. I'm supposed to calculate the Force of static friction on the flat surface to find the minimum force required for it to move then place that value into the equation (ignoring the cos angle).

oooh, lost me again :cry:
 
  • #7
Yes, forgot to state that the box was on a plank. Ignore my EDIT. So, if there were 2 boxes (each of different mass) with that same coefficient of static friction, would the angles at which each box starts to slide be the same?
Thanks :)
 
  • #8
Nicolaus said:
So, if there were 2 boxes (each of different mass) with that same coefficient of static friction, would the angles at which each box starts to slide be the same?

yes, mass and shape would make no difference :smile:

(btw, what have the nails to do with it? :confused:

is there a second part in which you're asked whether the box tips over?)
 
  • #9
No, nothing. It's just a problem using a construction site and 2 boxes of nails as the setting and objects, respectively. It says that there are 2 boxes (each of different mass) on a plank being raised by a crane and the static friction is .4, and asks us to find the angle at which each box starts to slide. We concluded that both would, logically, start to slide at the same angle since the the mass and gravitational constant cancel out in both cases when solving for the angle.
:)
 

1. What is force?

Force is a physical quantity that can cause a change in the motion or shape of an object. It is described as a push or pull on an object and is measured in Newtons (N).

2. What is static friction?

Static friction is a type of friction that occurs when two surfaces are in contact with each other but are not moving relative to each other. It acts in the opposite direction of an applied force and prevents the object from moving.

3. How is static friction different from kinetic friction?

Static friction occurs when an object is at rest, whereas kinetic friction occurs when an object is in motion. The magnitude of static friction is usually greater than kinetic friction, which makes it harder to start an object moving than to keep it moving.

4. What factors affect the amount of static friction?

The amount of static friction depends on the nature of the surfaces in contact, the normal force applied, and the roughness of the surfaces. It also depends on the coefficient of static friction, which is a measure of how easily the surfaces slide against each other.

5. How is the coefficient of static friction determined?

The coefficient of static friction is determined by conducting experiments and measuring the maximum force needed to start an object moving against a given surface. It is a dimensionless quantity and can vary depending on the materials in contact.

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