What is the maximum force to push a 50 kg wagon with a 15 kg box on an incline?

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The discussion revolves around calculating the maximum force required to push a 50 kg wagon up a 15-degree incline, which has a 15 kg box on top. The problem involves understanding the forces acting on both the wagon and the box, including friction coefficients and gravitational forces.

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  • Mixed

Approaches and Questions Raised

  • Participants discuss drawing free-body diagrams and summing forces for both the wagon and the box. There are attempts to clarify the forces acting on each object, including gravitational and frictional forces. Questions arise about the direction of friction and how to relate the forces acting on the wagon to the box.

Discussion Status

There is ongoing exploration of the problem with various interpretations of the forces involved. Some participants are attempting to clarify their reasoning and calculations, while others are questioning assumptions about the direction of forces and the application of friction. Guidance has been offered regarding the need to sum forces in different directions.

Contextual Notes

Participants express confusion about the application of forces and the role of friction, indicating a need for clearer definitions and understanding of the physics concepts involved. There is mention of potential gaps in knowledge from previous studies.

Fusilli_Jerry89
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a 50 kg wagon is being pushed up a 15 degree incline. The coefficient of friction between the wagon and the slope is 0.15. A 15 kg box sits on top of the wagon and the coefficient between the wagon and the box is 0.30. What is the maximum force that you can push the wagon up the slope with before the box starts to slide?
 
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Start by posting your current work on the problem.
 
well first i drew it and came up with:
F-127-71+42.6=50a for the wagon and concluded that an extra 4.6 N must be directed down the slope in order to move the box. I am clueless now.
 
Last edited:
How'd you get those numbers? Can you be a little more clear?
 
lol too much typing ok here I go
the 127 is the force of gravity acting on the big box down the slope, the 71 is the force of friction between the big box and the slope the 42.6 is the force of friction acting up on the wagon.
 
Sum the forces on the block in one free-body diagram, then sum the forces on the cart in another.

There should be no force of friction acting up the ramp on the wagon. The wagon's motion is upwards, and friction resists the direction of motion.

Once we have four equations from summing our forces, find a way to relate the maximum static friction between the block and cart to the force being applied to the cart. Plug in the maximum friction and get the maximum force.
 
Fusilli_Jerry89 said:
well first i drew it and came up with:
F-127-71+42.6=50a for the wagon and concluded that an extra 4.6 N must be directed down the slope in order to move the box. I am clueless now.

EthanB said:
Sum the forces on the block in one free-body diagram, then sum the forces on the cart in another.

There should be no force of friction acting up the ramp on the wagon. The wagon's motion is upwards, and friction resists the direction of motion.

Once we have four equations from summing our forces, find a way to relate the maximum static friction between the block and cart to the force being applied to the cart. Plug in the maximum friction and get the maximum force.

I put the force of friction acting down
 
If friction is acting down, we should be subtracting 42.6.
 
i am only able to come up with 2 equations: F-155.4=50a for the wagon and F=4.6 for the box. What else is there?
 
  • #10
isnt the 42.6 N acting upwards tho? bcuz the box isn't moving and the friction has to be acting upwards to keep it from moving.
 
  • #11
The friction between the box and wagon acts in different directions on each object. It acts downwards on the wagon and upwards on the box.

We can sum the forces up/down the ramp for each object, then perpendicular to the ramp for each object. Maybe you already took that into account and found numerical answers for everything. I haven't plugged the numbers and compared them to what you've gotten. My carpel tunnel is acting up and I'm going to sign off for the night. Good luck!
 
  • #12
What I don't get is how can you supply extra Newtons downwards without actually touch the box? The force of friction stays the same, this has to do with inertia but I have no idea how to solve for this? Maybe I missed something in Physics last year, could anyone help?
 
  • #13
Fusilli_Jerry89 said:
What I don't get is how can you supply extra Newtons downwards without actually touch the box? The force of friction stays the same, this has to do with inertia but I have no idea how to solve for this? Maybe I missed something in Physics last year, could anyone help?

I'm not sure what extra Newtons you're referring to. Lay out to me what you have and I will go from there. Try to be as specific as possible. Use a format such as:

Fx(on wagon) = Fa - Ff(ramp) ... etc.
 
  • #14
Sorry I don't understand that format, is Fx sposed to be parallel to the slope? and what is Fa?

For the wagon:
Ff = 70.95 N
Fg = 127 N
F = ?

For the box:
Ff = 42.6 N
Fg = 38 N
 
  • #15
If the x direction is parallel to the slope, Fx means the forces parallel to the slope.

I mean force applied by Fa.
 
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