PASCO ME-6843 Spring Cart Launcher - Manual (Page 3)

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M o d e l N o . M E - 6 8 4 3 C a r t M a s s
3
Cart Mass
For varying the mass of the cart, the Spring Cart Launcher is designed to hold one or
two Compact Cart Masses (PASCO part ME-6755). The launcher prevents these
masses from shifting or sliding. Place the masses as illustrated.
Theory
The spring constant of a spring is
(eq. 1)
where F
x
is the force applied to the spring and x is the displacement of the end of the
spring from its equilibrium position.
As you push the end of a spring (or anything else) from position x
1
to x
2
, the work that
you do is equal to the area under the F
x
versus x graph, or
(eq. 2)
The potential energy stored in a spring is
(eq. 3)
The kinetic energy of a cart moving on a track is
(eq. 4)
where m is the mass of the cart, and V is the magnitude of velocity.
The change in gravitational potential energy of a cart moving up an inclined track is
(eq. 5)
where g = 9.8 m/s 2 , ∆s is the distance traveled along the track (in the uphill direction),
and
θ is the track’s angle of incline.
Masses
k
F
x
x
------ =
Spring constant
W F
x
x d
x
1
x
2 ∫
=
Work done on a spring
U
spring
1
2
--- kx
2
=
Potential energy stored in
a spring
K
1
2
---m V
2
=
Kinetic energy
∆U
gravity
mg
∆s θ
sin =
Potential energy of a cart
on an inclined track