Calculate Arrow Speed & Height | Spring Energy Problem Homework

In summary, an archer exerts an average force of 192 N to draw a 0.30 kg arrow back 1.3 m. Neglecting air resistance, the arrow will leave the bow with a speed of 28.85 m/s. If shot straight up, the arrow will rise to a height of 42.4 m. However, in order to calculate the correct values, it is important to use the correct equations and take into account the average force and energy exerted.
  • #1
whoopie88
52
0

Homework Statement


An archer puts a 0.30 kg arrow to the bowstring. An average force of 192 N is exerted to draw the string back 1.3 m. Assume that air resistance is negligible.
(a) Assuming that all the energy goes into the arrow, with what speed does the arrow leave the bow?

(b) If the arrow is shot straight up, how high does it rise?

Homework Equations


All Energy/Work equations


The Attempt at a Solution


2hxo8pe.jpg


Thanks in advance for help!
 
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  • #2
Those values look correct to me.
 
  • #3
Really? o.o I'm doing a Webassign, and it's telling me that my values are incorrect.
I put in 28.85 m/s for (a) and 42.4 m for (b).

Is there something I'm missing? o.o
 
  • #4
whoopie88 said:
Really? o.o I'm doing a Webassign, and it's telling me that my values are incorrect.
I put in 28.85 m/s for (a) and 42.4 m for (b).

Is there something I'm missing? o.o

Given the values, it should be correct. Realistically speaking, 1.3 m is quite large for an archer to stretch the string.
 
  • #5
whoopie88 said:
Really? o.o I'm doing a Webassign, and it's telling me that my values are incorrect.
I put in 28.85 m/s for (a) and 42.4 m for (b).

Is there something I'm missing? o.o

The "average" force is F, so the energy is F * 1.3

or

F = 192 = K* X /2 not K * X

So the velocity is 28.85 * sqrt(2) = 40.8m/sec
 

1. What is the "Spring Energy Problem"?

The "Spring Energy Problem" is a physics problem that involves calculating the potential and kinetic energy of a spring that is stretched or compressed from its equilibrium position. It is a common problem in introductory physics courses.

2. How do you solve the "Spring Energy Problem"?

To solve the "Spring Energy Problem", you need to know the spring constant (k) and the displacement of the spring from its equilibrium position (x). You can then use the formula for potential energy (U = 1/2 kx^2) and the formula for kinetic energy (K = 1/2 mv^2) to calculate the total energy of the spring.

3. What is the importance of the "Spring Energy Problem"?

The "Spring Energy Problem" is important because it helps us understand the relationship between potential and kinetic energy and how they change as a spring is stretched or compressed. It also allows us to apply these concepts to real-world situations, such as in the design of springs for various applications.

4. What are some common variations of the "Spring Energy Problem"?

Some common variations of the "Spring Energy Problem" include using different types of springs (e.g. non-linear springs), adding external forces to the system, and considering the effects of friction on the motion of the spring.

5. How can the "Spring Energy Problem" be applied in the real world?

The "Spring Energy Problem" can be applied in various real-world scenarios, such as in the design and testing of springs for use in machinery, car suspensions, and even in sports equipment like trampolines. It can also be used to understand the energy transformations in systems involving springs, such as in simple harmonic motion.

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