Solving a 5kg Object's Frictionless Pipe Homework

In summary, the problem involves a 5-kg object sliding with an initial speed V0 in a hollow frictionless pipe. The object makes contact with two nested springs, with the inner spring having a spring constant of 200 N/m. The decrease in kinetic energy as the object moves from point A to point B can be calculated using energy conservation, where the work done on the spring is stored as potential energy. The additional decrease in kinetic energy as the object moves from point B to point C can also be calculated using energy conservation. The initial speed V0 of the object can be found using the given information. The spring constant of the outer spring can be calculated using the same method as the inner spring.
  • #1
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Homework Statement


A 5-kg object initially slides with speed V0 in a hollow frictionless pipe. The end of the pipe contains two springs, one nested inside the other, as shown above. The object makes contact with the inner spring at point A, moves 0.1 meter to make contact with the outer spring at point B, and then moves an additional 0.05 meter before coming to rest at point C. The graph shows the magnitude of the force exerted on the object by the springs as a function of the object's distance from point A.
a. Calculate the spring constant for the inner spring.​
b. Calculate the decrease in kinetic energy of the object as it moves from point A to point B.​
c. Calculate the additional decrease in kinetic energy of the object as it moves from point B to point C.​
d. Calculate the initial speed V0 of the object.​
e. Calculate the spring constant of the outer spring.​

m = 5 kg
ΔxA-B = 0.10 m
ΔxB-C = 0.05 m
Vat C = 0 m/s

(Here are the diagram and the graph. Sorry if they're less than beautiful, I just quickly recreated them on MS Paint)

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Homework Equations



F=kx
Uelastic=(1/2)kx2
Kinematic Equations

The Attempt at a Solution



According to the graph, F=20 N when the object is at B, and it's displacement at B (relative to the point at which it first made contact with the inner spring) is 0.10 m. So:
F = kx
20N = k(0.10m)
k = 200 N/m

As for part b, I don't really know where to start. Would I calculate Uelastic to find the decrease in kinetic energy? I have no idea how to do c, d, or e, either...
 
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  • #2


Use energy conservation. The loss in kinetic energy corresponds to an increase in the potential energy due to the spring.
 
  • #3


According to the graph, F=20 N when the object is at B, and it's displacement at B (relative to the point at which it first made contact with the inner spring) is 0.10 m. So:
F = kx
20N = k(0.10m)
k = 200 N/m
----------
F is not constant.
You can find work done on the spring, Fx, as an area under the graph.
The work done on the spring is stored as potential energy, 1/2 kx2
 

1. How do I calculate the force required to move a 5kg object through a frictionless pipe?

In order to calculate the force required to move a 5kg object through a frictionless pipe, you will need to use the equation F=ma, where F is the force, m is the mass of the object, and a is the acceleration. Since the pipe is frictionless, the acceleration will be constant and equal to the force divided by the mass. Therefore, the force required will be 5kg multiplied by the desired acceleration.

2. What is the purpose of solving a 5kg object's frictionless pipe homework?

The purpose of solving a 5kg object's frictionless pipe homework is to understand the concept of friction and how it affects the movement of objects. By solving this problem, you will also gain practice in using equations and applying them to real-world scenarios. This will help you develop problem-solving skills, which are essential for a scientist.

3. How does the weight of the object affect the force needed to move it through a frictionless pipe?

The weight of an object does not affect the force needed to move it through a frictionless pipe. This is because weight is a measurement of mass multiplied by the force of gravity, and in a frictionless environment, there is no force of gravity acting on the object. Therefore, the only factor that affects the force needed is the mass of the object itself.

4. Can the force required to move a 5kg object through a frictionless pipe ever be zero?

Yes, the force required to move a 5kg object through a frictionless pipe can be zero. In a frictionless environment, there is no external force acting on the object, so the only force needed to move it would be the initial force to set it in motion. Once the object is in motion, it will continue to move with the same velocity unless acted upon by an external force.

5. What are some real-life applications of understanding friction in a frictionless pipe?

Understanding friction in a frictionless pipe has several real-life applications. For example, this concept is essential in designing machinery and transportation systems that require smooth and efficient movement. It is also crucial in fields such as fluid mechanics and aerodynamics, where minimizing friction is key to maximizing efficiency. Additionally, understanding friction can help in the development of new technologies and materials that reduce friction and improve performance.

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