The document discusses simple harmonic motion using a slingshot as an example. It provides information about a boy pulling back the rubber band of his slingshot 25 cm before releasing a pebble. The slingshot has a spring constant of 250 N/m. It then asks two questions: 1) what is the energy of the pulled back rubber band, and 2) if the slingshot mass is 10g, what is the speed of the pebble as it leaves the rubber band. The answers are then provided: 1) the energy is 7.8 J, and 2) the speed is 39.5 m/s. Visualizations and equations are shown to explain the workings.

1. Energy in Simple
Harmonic Motion
Pebble and slingshot
Carla Obando
33027129

2. Pebble and slingshot
question:
• A little boy pulls on the rubber band of his slingshot
by 25 cm before releasing the pebble. The slingshot
has a spring constant of 250 N/m.
• Question 1: What is the energy of the pulled back
rubber band?
• Question 2: If the slingshot has a mass of 10 g, what
is the speed of the pebble as it leaves the rubber
band?

3. ANSWERS:
• Question 1: 7.8 J
• Question 2: 39.5 m/s

4. Let’s Visualize it !
A little boy pulls on the rubber band of his slingshot by 25 cm before releasing the pebble. The
slingshot has a spring constant of 250 N/m.
Question 1: What is the energy of the pulled back rubber band?
Image taken from
http://media2.hickorees.c
om/image/SlingShot_L7.j
pg

5. Solution:
A little boy pulls on the rubber band of his slingshot by 25 cm before releasing the pebble. The
slingshot has a spring constant of 250 N/m.
Question 1: What is the energy of the pulled back rubber band?
• Question 1:
Total Energy when it rubber band is pulled :
E = (K) + (U)
E = (1/2)mv^2 + (1/2)kx^2
 Because a hand is holding onto the rubber
when it is pulled, let v=0, k=250N/m, and x=0.25m
Plug it in the equation:
E = (1/2)m(0)^2 + (1/2)(250)(0.25)^2
E = 0 + 7.8
The energy when the rubber band is pulled is
7.8 J which is potential energy while kinetic energy
is 0 because velocity is also 0

6. Solution:
A little boy pulls on the rubber band of his slingshot by 25 cm before releasing the pebble. The
slingshot has a spring constant of 250 N/m.
Question 2: If the slingshot has a mass of 10g, what is the speed of the pebble as it leaves the rubber
band?
• Question 2:
 Key concept: The speed of the pebble when it
leaves the rubber band is the maximum speed
that the pebble is moving.
The equation we use is :
Vm = sqrt(2E/m)
Given the slingshot’s mass of 0.01 kg
Vm = sqrt((2*7.8)/0.01)
Vm = 39.5 m/s

7. THANKS!