Help with elastic potential energy

AI Thread Summary
To find the speed of the dart as it leaves the toy, use the principle that elastic potential energy (Ee) equals kinetic energy (Ek). The formula for Ee is 1/2 k x^2, where k is the spring constant and x is the compression distance. The kinetic energy formula is 1/2 mv^2, where m is the mass of the dart. By equating these two energies and solving for v, you can determine the dart's speed using the provided values. This approach effectively utilizes the relationship between potential and kinetic energy in the context of the problem.
jbjohnybaker
Messages
19
Reaction score
0

Homework Statement



A child's toy shoots a rubber dart of mass 7.8g, using a compressed spring with a force constant of 3.5 x 10^2 N/m. The spring is initially compressed 4.5cm. All the elastic potential energy is converted into kinetic energy of the dart.
What is the speed of the dart as it leaves the toy?


Homework Equations


Ee = Ek
Ee = 1/2 k x^2
Ek = 1/2 mv^2

The Attempt at a Solution


Ee = Ek
1/2 (3.5 x10^2)(?) = 1/2 (.0078)v^2 ??]
 
Physics news on Phys.org


jbjohnybaker said:

Homework Statement



A child's toy shoots a rubber dart of mass 7.8g, using a compressed spring with a force constant of 3.5 x 10^2 N/m. The spring is initially compressed 4.5cm. All the elastic potential energy is converted into kinetic energy of the dart.
What is the speed of the dart as it leaves the toy?


Homework Equations


Ee = Ek
Ee = 1/2 k x^2
Ek = 1/2 mv^2

The Attempt at a Solution


Ee = Ek
1/2 (3.5 x10^2)(?) = 1/2 (.0078)v^2 ??]
How much is the spring compressed?

http://www.physics247.com/physics-tutorial/spring-potential-energy.shtml"
 
Last edited by a moderator:


equating Ee to Ek is indeed the right way to go. I suggest writing that equation in symbols (not yet plugging in the numbers) and then solving for v.
You'll get an expression for v in terms of k (spring constant), m (mass of the dart) and x (initial compression of the spring), all of which are given.
Then you simply plug in the given values and compute the value for v.

Alex
 
Thread 'Struggling to make relation between elastic force and height'
Hello guys this is what I tried so far. I used the UTS to calculate the force it needs when the rope tears. My idea was to make a relationship/ function that would give me the force depending on height. Yeah i couldnt find a way to solve it. I also thought about how I could use hooks law (how it was given to me in my script) with the thought of instead of having two part of a rope id have one singular rope from the middle to the top where I could find the difference in height. But the...
I treat this question as two cases of Doppler effect. (1) When the sound wave travels from bat to moth Speed of sound = 222 x 1.5 = 333 m/s Frequency received by moth: $$f_1=\frac{333+v}{333}\times 222$$ (2) When the sound wave is reflected from moth back to bat Frequency received by bat (moth as source and bat as observer): $$f_2=\frac{333}{333-v}\times f_1$$ $$230.3=\frac{333}{333-v}\times \frac{333+v}{333}\times 222$$ Solving this equation, I get ##v=6.1## m/s but the answer key is...
Back
Top