Solving an Elastic Force & Energy Homework Problem

In summary, we have found the spring constant K, the elastic energy (Ue), and the speeds of the arrow and marker using the given information and equations.
  • #1
anahvajyo5
1
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Homework Statement


This is a two part question.
the graph is a force as a function of displacement
first mass of an arrow= .002 kg
marker= .01154 kg
delta x= 0.7
while x = 0.15.
the coordinate points are (0,0) and (0.15, 9.5)

1. Find K
2. Find elastic energy (Ue)
3. Find speed for the arrow and marker


Homework Equations





The Attempt at a Solution


I tried using K= (mg)/x
for both but i got :
arrow= k= 0.1308

and marker = K= 0.7547
is this right?
how do yo ufigure out the rest?
 
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  • #2


I would first check your calculations to make sure they are correct. It is also important to include units in your answer, as that can help with verifying the correctness of your calculations.

1. To find K, you can use the equation K = (mg)/x, where m is the mass and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values given, we get:

K = (0.002 kg + 0.01154 kg)(9.8 m/s^2) / 0.7 m = 0.206 N/m

2. To find the elastic energy (Ue), you can use the equation Ue = (1/2)Kx^2, where K is the spring constant and x is the displacement. Plugging in the values given, we get:

Ue = (1/2)(0.206 N/m)(0.7 m)^2 = 0.050 Nm or 0.050 J

3. To find the speed of the arrow and marker, we can use the equation v = √(2Ue/m), where Ue is the elastic energy and m is the mass. Plugging in the values, we get:

v for arrow = √(2(0.050 J) / 0.002 kg) = 7.07 m/s
v for marker = √(2(0.050 J) / 0.01154 kg) = 3.88 m/s

I hope this helps! Let me know if you have any further questions or if you would like me to explain anything in more detail.
 

1. How do I solve for the elastic force in a given problem?

To solve for the elastic force, you will need to use the equation F = kx, where F is the force, k is the spring constant, and x is the displacement of the object. Make sure to plug in the correct values for each variable and solve for the force.

2. What is the difference between elastic potential energy and elastic force?

Elastic potential energy is the energy stored in an object when it is compressed or stretched, while elastic force is the force that is exerted by a spring or elastic material when it is stretched or compressed. In other words, elastic potential energy is a form of potential energy, while elastic force is a physical force.

3. How do I determine the spring constant in a problem?

The spring constant, denoted as k, can be determined by dividing the force by the displacement. In other words, k = F/x. Alternatively, you can also use Hooke's law, which states that the spring constant is equal to the force divided by the change in length of the spring.

4. Can I solve an elastic force and energy homework problem without knowing the spring constant?

Yes, it is possible to solve an elastic force and energy problem without knowing the spring constant. You can use Hooke's law, F = kx, to solve for the force without knowing the value of k. You can also use the equation for elastic potential energy, U = 1/2 kx², to solve for the potential energy without knowing the spring constant.

5. Are there any common mistakes to avoid when solving an elastic force and energy homework problem?

One common mistake to avoid is forgetting to convert units. Make sure to use consistent units for force, displacement, and spring constant. Another mistake to avoid is using the wrong formula. Double check which formula is appropriate for the given problem. Lastly, make sure to solve for the correct variable based on the given information.

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