Force on a Box - Find Weight

In summary, the problem involves pushing a box at a 15° angle below the horizontal with a force of 650 N on a horizontal surface with a coefficient of static friction of 0.7. To determine the heaviest box that can be moved, the equation 650cos15 = [((\mu)(9.80)(m))+((\mu)(650sin15))] is used, taking into account the vertical force component and multiplying the coefficient of friction to both the weight and 650sin15.
  • #1
erok81
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Homework Statement



You push down on a box at an angle 15° below the horizontal with a force of 650 N. If the box is on a horizontal surface and the coefficient of static friction is 0.7, what is the heaviest box you will be able to move?

Homework Equations



F=ma

The Attempt at a Solution



So I've solved this problem using Fnet which was 650cos15 for the horizontal force and then subtracted [tex](\mu_s)(9.80)(m)[/tex] The ma part goes to zero since it's not accelerating.

Therefore I get [tex]650cos15 = (\mu)(9.80)(m)[/tex] and then solve for m.

I thought that was it. But now that I thinking about it more, there is a vertical component for the force. I'd imagine that extra force would make the box seem to weigh more, thereby increasing friction, making the box weigh less.

Do I factor that vertical force in? If so, how?
 
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  • #2
Ah! Maybe like this?

[tex]650cos15 = [((\mu)(9.80)(m))+(650sin15)[/tex]

All I did here was add in the vertical force component to the friction.

Yeah...that isn't right since my box ends up weighing 2kg.
 
Last edited:
  • #3
Your above equation is correct.Though you will multiply the coefficient of friction to both the weight as well as 650sin15
 
  • #4
Nice.

So something like this?


[tex]650cos15 = [((\mu)(9.80)(m))+((\mu)(650sin15))][/tex]
 
  • #5
Yeah,that's correct.
 
  • #6
Thanks for the help!:approve:
 

1. How do you calculate the weight of a box?

To calculate the weight of a box, you need to know the mass of the box and the acceleration due to gravity. The formula for weight is weight = mass x acceleration due to gravity. In most cases, the acceleration due to gravity is 9.8 m/s^2. So, to find the weight of a box, you would multiply the mass of the box (in kilograms) by 9.8.

2. What is the difference between weight and mass?

Weight and mass are often used interchangeably, but they are not the same thing. Mass refers to the amount of matter in an object, while weight is a measurement of the force of gravity acting on an object. Mass is measured in kilograms, while weight is measured in newtons.

3. How does the force of gravity affect the weight of a box?

The force of gravity is what gives objects weight. The greater the force of gravity, the greater the weight of an object will be. This means that on Earth, where the force of gravity is 9.8 m/s^2, a box will have a different weight than on the moon, where the force of gravity is only 1.62 m/s^2.

4. Can the weight of a box change?

Yes, the weight of a box can change depending on its location. As mentioned earlier, the force of gravity varies depending on the location. Additionally, the weight of a box can change if its mass changes, such as by adding or removing items from the box.

5. How is the weight of a box important in everyday life?

The weight of a box is important in everyday life because it affects how we interact with objects and how we move them. For example, knowing the weight of a box can help determine if it can be safely lifted and moved by one person or if it requires multiple people. In industries that involve shipping and transportation, knowing the weight of boxes is crucial for ensuring safe and efficient delivery.

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