PASCO ME-6950 PAScar with Mass - Manual (Page 20)

012-07361B PAScar with Mass
19
Experiment 6: Sliding Friction and
Conservation of Energy
EQUIPMENT NEEDED:
– PAScar (ME-6950) – Stopwatch (SE-8702)
– Metric tape (SE-8712A) – Brick or block of wood
– Long board that can be used as a ramp – Friction block (003-04708)
– Protractor
Purpose
In this lab, the PASCar will be launched down a ramp, as
shown in Figure 6.1, while riding on a friction block. The
initial elastic potential energy and gravitational potential
energy of the car are converted to thermal energy as the car
slides to a stop. The thermal energy generated on the surfaces
is the same as the work done against sliding friction.
Theory
Using the principle of conservation of energy, we can equate
the initial energy of the system with the final (i.e. thermal) energy of the system. This leads to:
1/2kx 2 + mgDsin
θ = µ
k
mgDcos
θ
(elastic P.E.) + (Gravitational P.E.) = (work done against friction)
where k is the spring constant of the plunger (from Experiment 4), x is the distance that the
plunger is pushed in, m is the mass of the car plus the friction block, D is the distance that the
block slides after the car’s plunger is released,
θθθθθ is the angle of the ramp to the horizontal, and
µ
k
is the coefficient of kinetic or “sliding” friction.
In this experiment, you will use the principle of the conservation of energy to predict D, given
certain measurements you will make and the value of k determined in Experiment 4. First you
will need to determine the coefficient of kinetic or “sliding” friction for the friction block.
Determining µ
k
: If the angle of the ramp is high enough, the friction block will slide
down the ramp with uniform acceleration, due to a net force on the block. The net force
on the block is the difference between the component of the gravitational force (mgsinø)
that is parallel to the surface of the ramp and the friction force (-µ
k
mgcosø) that retards
the motion. The angle ø is the angle of the ramp when the block slides down the ramp
with uniform acceleration. The acceleration down the ramp is given by:
a = mgsinø
- µ
k
mgcosø
The average acceleration down the ramp is given by:
a = 2d/t 2
where d is the total distance the block slides and t is the time required to slide through that
distance. If the acceleration is uniform, EQN-2 equals EQN-3. You can use the measured
values of the angle ø (the angle of uniform acceleration), the distance d, and the time t to
calculate the kinetic coefficient of friction µ
k
.
Figure 6.1
Friction block
(EQN-1):
(EQN-2):
(EQN-3):
θ