Calculating Potential and Kinetic Energy in a Slingshot Physics Problem

In summary, a slingshot is made up of a leather cup and two parallel rubber bands. It takes a force of 15 N to stretch each band 1.0 cm. When a 50-g stone is placed in the cup and pulled back 0.20 m, the potential energy stored in the bands is 60 J. The stone leaves the slingshot with a speed of 49 m/s. To find the answers, the equations F=kx and PE=1/2kx^2 were used.
  • #1
stanton
74
0

Homework Statement



A slingshot consists of a light leather cup, containing a stone, that is pulled back against two parallel rubber bands. It takes a force of 15 N to stretch either one of these bands 1.0 cm.

(a) What is the potential energy stored in the two bands together when a 50-g stone is placed in the cup and pulled back 0.20 m from the equilibrium position?

(b) With what speed does the stone leave the slingshot?

The answers are a) PE = 60 J b) v = 49 m/s

Homework Equations



F=kx PE=1/2kx^2

The Attempt at a Solution



a)
F=kx
15 = k(0.01) → k=1500 N/m

PE = 1/2 k x^2
= 1/2 (1500)(.20)2
= 30 J

b)
PE1=KE1, KE = 1/2mv^2
1/2mv^2 = 30
1/2(0.050)v^2 = 30;
v= 34.6 m/s

Any comment or help would be appreciated about why I got the answers wrong. Thank you.
 
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  • #2
Ok, I realized what was wrong with the first question. Since there are two straps, 30 must be doubled.
 
  • #3
Just remember, although you fixed your result for part A, you use it to answer part B. (In other words you have to make changes to part B as well)
 
  • #4
Thank you so much. :)
 

Related to Calculating Potential and Kinetic Energy in a Slingshot Physics Problem

1. How does a slingshot work?

A slingshot works by using potential energy stored in the stretched rubber bands to accelerate a projectile, which then converts into kinetic energy as it is released.

2. What factors affect the distance a slingshot can launch a projectile?

The distance a slingshot can launch a projectile is affected by factors such as the tension of the rubber bands, the mass and shape of the projectile, and the angle at which the slingshot is held.

3. Can a slingshot launch a projectile into orbit?

No, a slingshot is not capable of launching a projectile into orbit. It does not have enough velocity or control to overcome the Earth's gravity and enter a stable orbit.

4. How does the slingshot affect the trajectory of the projectile?

The slingshot affects the trajectory of the projectile by providing an initial force and direction. The angle at which the slingshot is held and the tension of the rubber bands determine the initial velocity and direction of the projectile.

5. Is the trajectory of a projectile from a slingshot affected by air resistance?

Yes, the trajectory of a projectile from a slingshot is affected by air resistance. As the projectile moves through the air, it experiences air resistance which slows it down and changes its trajectory.

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