Solving a 100kg Crate Pulled Across a Floor

  • Thread starter Gentec
  • Start date
In summary, to find the force P needed to pull a 100kg crate across a horizontal floor with a coefficient of kinetic friction of 0.200, we can use the equations P cos(30) = \mu N and N + P sin(30) = mg, where N is the normal force and mg is the weight of the crate. These equations ensure that the net work done is zero, resulting in a solution of 226.3N for P.
  • #1
Gentec
7
0
Good evening.

I would appreciate if someone could verify the following please.

The question:

A 100kg crate is pulled across a horizontal floor by a force P that makes an angle of 30 degrees above the horizontal. The coefficient of kinetic friction between the crate and floor is 0.200. What is P if the net work done is zero.

My solution:

First determine Ff = umg. This would give me 196N. My next step is to determine P. I use 196N and put that over cos30. My answer is 226.3N. Does this seem reasonable.

thanks for your time
 
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  • #2
Gentec said:
First determine Ff = umg.
No, [itex]F_f = \mu N[/itex], where N is the normal force. To solve this problem, recognize that the crate is in equilibrium. Set up equations for the vertical and horizontal forces. (Net force in each direction equals zero.)
 
  • #3
Thanks for the direction.

Is this what you meant?
Horizontal:
mgsin30 = f + Fcos30 = uN + Fcos30
Vertical:
N = Fsin30 = mgcos30

To resolve = Add N into N in equation for Horizontal
 
  • #4
I don't understand how you got your equations. Here's what I get:
Horizontal: [itex]P cos(30) = \mu N[/itex]
Vertical: [itex]N + P sin(30) = mg[/itex]
 

1. How do you calculate the force required to move a 100kg crate across a floor?

In order to calculate the force required to move a 100kg crate across a floor, you will need to use the equation F = m x a, where F is the force, m is the mass of the crate, and a is the acceleration. In this case, the acceleration can be assumed to be 0 since the crate is being pulled at a constant velocity across the floor. Therefore, the force required would simply be the product of the mass (100kg) and the acceleration (0), resulting in a force of 0 Newtons.

2. What factors can affect the force required to move a 100kg crate across a floor?

There are several factors that can affect the force required to move a 100kg crate across a floor, including the coefficient of friction between the crate and the floor, the type of surface the crate is being pulled on, and the angle at which the crate is being pulled. Additionally, the force required may also be affected by external forces such as air resistance or the force exerted by the person pulling the crate.

3. How can you decrease the force required to move a 100kg crate across a floor?

There are a few ways to decrease the force required to move a 100kg crate across a floor. One way is to use a lubricant, such as oil or grease, to reduce the coefficient of friction between the crate and the floor. Another way is to use a smoother surface, such as a polished floor, which will also reduce friction. Additionally, pulling the crate at an angle rather than straight across the floor can also decrease the force required.

4. What are some real-world applications of solving a 100kg crate pulled across a floor?

The calculation of force required to move a 100kg crate across a floor can be applied in various real-world scenarios, such as in the transportation industry. For example, when determining the force required to pull a loaded trailer on a road, engineers must consider the weight of the trailer and the friction between the tires and the road surface. This calculation can also be useful in designing pulley systems, as well as in understanding the forces involved in moving heavy objects in manufacturing or construction settings.

5. How can this calculation be used to ensure safety when moving a 100kg crate across a floor?

By calculating the force required to move a 100kg crate across a floor, safety measures can be put in place to prevent accidents or injuries. For instance, knowing the force required can help determine the number of people needed to safely move the crate or if additional tools, such as a dolly or forklift, should be used. It can also help identify potential hazards, such as a surface with too much friction, which can be addressed to ensure safe movement of the crate.

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