How Far Will a Cart Roll on Sand and Gravel? | Work/Energy Question

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In summary: Since the work done is force times distance, and we know the force for both cases, we can solve for the distance traveled for the gravel patch. In summary, the cart exerts an average horizontal force of 6 N and travels 6 cm through sand before stopping. When encountering gravel, the cart exerts a force of 9 N and will travel a distance of 4 cm before coming to a stop. This is determined by setting the work done to stop the cart equal to the force times distance and solving for the distance.
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bdh2991
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Homework Statement



A cart is set rolling across a level table, at the same speed
on every trial. If it runs into a patch of sand, the cart exerts
on the sand an average horizontal force of 6 N and travels
a distance of 6 cm through the sand as it comes to a stop.
If instead the cart runs into a patch of gravel on which
the cart exerts an average horizontal force of 9 N, how far
into the gravel will the cart roll before stopping? (a) 9 cm
(b) 6 cm (c) 4 cm (d) 3 cm (e) none of those answers

Homework Equations



w = ΔK.E.

The Attempt at a Solution



I basically found that 6N(.06) = .36 J for the sand part of it and set that answer to 9N * x = .36J and got the right answer but i don't know if i got the right answer because of the right reasons. My thinking was that if the mass and velocity of both carts are the same then the change in kinetic energy is ultimately going to be the same but I'm not to sure about this
 
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  • #2
you've got the right idea. In both cases, the KE of the cart is the same, so the work done to stop the cart is the same in both cases.
 

Related to How Far Will a Cart Roll on Sand and Gravel? | Work/Energy Question

1. How does the surface of sand and gravel affect the distance a cart will roll?

The surface of sand and gravel can significantly affect the distance a cart will roll. Sand is a loose, granular surface that provides less resistance to the cart's movement, allowing it to roll further. Gravel, on the other hand, is a coarser surface with larger particles, creating more friction and resistance, causing the cart to roll a shorter distance.

2. Why does the mass of the cart impact the distance it can roll on sand and gravel?

The mass of the cart affects the distance it can roll on sand and gravel because it determines the cart's inertia. A heavier cart will have more inertia and require more force to move, making it harder to roll on sand and gravel. A lighter cart will have less inertia and require less force to move, allowing it to roll further.

3. What is the role of work and energy in determining how far a cart will roll on sand and gravel?

Work and energy are crucial factors in determining how far a cart will roll on sand and gravel. Work is the transfer of energy to an object to make it move, while energy is the ability to do work. In this scenario, the work done on the cart is converted into kinetic energy, which allows the cart to roll. The surface of sand and gravel will affect the work done and the energy transferred, ultimately impacting the distance the cart can roll.

4. Can the angle of the incline affect how far a cart will roll on sand and gravel?

Yes, the angle of the incline can affect how far a cart will roll on sand and gravel. If the incline is steep, it will require more work to move the cart, resulting in less energy being transferred to allow the cart to roll. On the other hand, a gentle incline will require less work and allow the cart to roll further.

5. Is there a maximum distance that a cart can roll on sand and gravel?

Yes, there is a maximum distance that a cart can roll on sand and gravel. This distance will depend on various factors such as the mass and shape of the cart, the surface of the sand and gravel, and the force applied to move the cart. In general, the distance a cart can roll will decrease as the surface becomes rougher and the mass of the cart increases.

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