Using Work Energy Theorem to Find Necessary Velocity

In summary, the problem involves pushing a box up an incline plane with a constant angle and reaching a person waiting to receive it at a distance vertically above. The slope is slippery and has a small amount of friction with kinetic friction coefficient μk. Using the work-energy theorem, the minimum speed required to push the box to the receiver can be expressed as the square root of 2gh(1+μk/tan(a)), where g is the force of gravity, h is the distance, μk is the kinetic friction coefficient, and a is the angle of the incline. The work-energy theorem states that the work done by all forces acting on an object is equal to the change in kinetic energy of the object. In this
  • #1
Thenotsophysicsguy
3
0
1. The problem statement, all variables and given/
You must push a box up an incline plane (the angle being constant : a), to a person waiting to receive it, who is a distance of h(constant) vertically above you. Though the slope is slippery, there is a small amount of friction with kinetic friction coefficient μk. Use the work-energy theorem to determine the minimum speed at which you must push the box, so that it may reach the receiver. Express answer in terms of g, h, μk, and a

Homework Equations


Among many equations there are:
Fk=μk*Fn (FN being natural force)
Force of Gravity=mg

The Attempt at a Solution


I know that the answer is the square root of 2gh(1+μk/tan(a)), but I am not fully sure what the steps are to reaching this conclusion.
 
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  • #2
What have you tried? What does the work-energy theorem say? What are the types of energy involved here?
 
  • #3
I thought the wording of this problem was a little vague. Just to clarify, the person at the bottom gives the box a shove, and releases it at an initial velocity such that the box slides up the incline (without any additional pushing) and just barely makes it to the top.
 
  • #4
exactly
 

FAQ: Using Work Energy Theorem to Find Necessary Velocity

What is the Work Energy Theorem?

The Work Energy Theorem is a principle in physics that states that the work done on an object is equal to the change in its kinetic energy. In other words, the net work done on an object will result in a change in its velocity.

How is the Work Energy Theorem applied to find necessary velocity?

To find the necessary velocity using the Work Energy Theorem, you would first need to determine the initial and final kinetic energies of the object. Then, using the formula KE = 1/2mv^2, you would plug in the values and solve for the velocity.

Can the Work Energy Theorem be used to find velocity in any situation?

No, the Work Energy Theorem can only be used in situations where the only forces acting on the object are conservative forces, such as gravity or elastic forces. It is also important to note that the theorem only applies to point masses, and not objects with rotational or other types of motion.

What are some real-world applications of using the Work Energy Theorem to find necessary velocity?

The Work Energy Theorem is commonly used in areas such as engineering and mechanics, where it can be used to calculate the necessary velocity for objects in motion, such as cars, airplanes, and projectiles. It is also used in sports, such as calculating the necessary velocity to clear a high jump or make a successful ski jump.

Are there any limitations to using the Work Energy Theorem to find necessary velocity?

Yes, there are some limitations to using the Work Energy Theorem. As mentioned before, it can only be used in situations where conservative forces are the only ones acting on the object. It also does not take into account factors such as air resistance or friction, which can affect the actual velocity of an object in motion. In these cases, more complex equations or models may be required.

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