Towing two stacked boxes up a ramp

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In summary, towing two stacked boxes up a ramp involves applying force to move the boxes against gravity, ensuring stability and balance during the ascent. Proper technique and equipment are essential to prevent slippage and maintain control throughout the process.
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Sebee_ulg
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Homework Statement
A man pulls two boxes along a ramp of length L = 4.75 m and height H = 2.5 m. To do this, he pulls on a rope attached to the first box of mass m1 = 48 kg. The second box has a mass m2 = 32 kg and is placed on top of the first. The coefficient of friction between the first box and the floor is µ1 = 0.444 and the coefficient of friction between the two boxes is µ2 = 0.8.
Relevant Equations
(a) the force to be applied to move the two boxes at a constant speed constant v = 1.5 m/s. (b) the maximum force that can be applied to the string to ensure that the two boxes to remain stationary relative to each other. (c) What will be the speed of the boxes after travelling 1 m?
Answer is (a) F ≃ 675 (N); (b) F ≃ 859 (N) (c) v ≃ 2.2 (m/s).
 
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  • #4
Sebee_ulg said:
Sorry, I hadn't read the instructions and my question is that I can't find the right result for question b.
Mainly: what is your best effort ?

And: what are the relevant equations you need to get going on this exercise ?

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  • #5
Sebee_ulg said:
Sorry, I hadn't read the instructions and my question is that I can't find the right result for question b.
Have you drawn Free Body Diagrams for both boxes?
If they do not stay together, what can you say about the forces between them?
 

FAQ: Towing two stacked boxes up a ramp

What factors affect the force needed to tow two stacked boxes up a ramp?

The force needed to tow two stacked boxes up a ramp depends on several factors: the combined weight of the boxes, the angle of the ramp, the coefficient of friction between the boxes and the ramp, and any additional forces such as tension in the towing rope. These factors collectively determine the overall resistance that must be overcome to move the boxes upward.

How do you calculate the force required to move the boxes up the ramp?

To calculate the force required to move the boxes up the ramp, you can use the equation F = (m1 + m2) * g * (sin(θ) + μ * cos(θ)), where m1 and m2 are the masses of the two boxes, g is the acceleration due to gravity, θ is the angle of the ramp, and μ is the coefficient of friction. This equation takes into account both the gravitational component pulling the boxes down the ramp and the frictional force resisting the motion.

How does the angle of the ramp influence the towing process?

The angle of the ramp significantly influences the towing process. As the angle increases, the component of gravitational force acting parallel to the ramp's surface also increases, making it more difficult to tow the boxes upward. Conversely, a smaller angle reduces this component, making the towing process easier. The angle also affects the normal force, which in turn influences the frictional force.

What role does friction play in towing the boxes up the ramp?

Friction plays a crucial role in towing the boxes up the ramp. It acts as a resistive force that opposes the motion of the boxes. The coefficient of friction between the boxes and the ramp surface determines the magnitude of this resistive force. Higher friction means more force is required to tow the boxes, while lower friction makes the towing easier. Both static and kinetic friction can be relevant, depending on whether the boxes are initially at rest or already in motion.

Can the boxes slip or topple while being towed up the ramp, and how can this be prevented?

Yes, the boxes can slip or topple while being towed up the ramp if the forces acting on them are not properly balanced. To prevent slipping, ensure that the frictional force is sufficient to counteract the component of gravitational force pulling the boxes down the ramp. To prevent toppling, maintain a low center of gravity by stacking the boxes securely and ensuring that the towing force is applied steadily and evenly. Additionally, using straps or other securing methods can help keep the boxes stable during the towing process.

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