Calculations
After constructing the actual machine, we required to explore some of the physics behind the parts. This included calculating the work down by the simple machines, the mechanical advantages, the amount of force that was being applied and the resultant output force, velocities, accelerations, et cetera. This is where we truly demonstrated our understanding of what had been learned in the current unit. The calculations for each step are as follows:
Step 1 The Class Two Lever:
For the step that initiated the machine, we calculated the amount of work the lever did:
Work= Force times distance
W= 0.25 N x 13 cm
W= 3.25 J
Step 2 The Marble's Velocity:
As the marble rolled down the first inclined plane, we found it's velocity:
Velocity= distance/time
V=61 cm/0.62 sec
V=98.39 cm/sec or 0.98 m/sec
Step 3 Mechanical Advantage of the Second Inclined Plane:
Our first mechanical advantage calculation was for the second inclined plane:
Mechanical Advantage= input distance/output distance
MA= 34 cm/12 cm
MA= 2.83
Step 4 Mechanical Advantage of the Pulley System:
This step required no calculation, just simple knowledge of pulleys:
One pulley system has a mechanical advantage of 1.
Step 5 Force Exerted by the Wedge:
In this step, a golf ball is held in place by a simple machine called a wedge.
Force= mass times acceleration/mechanical advantage of ramp
F= 0.0475 kg x 10 m/s squared/ 10
F= 0.0475 N
Step 6 Acceleration of the Golf Ball:
For the sixth step, our calculation focused on the acceleration of the golf ball as it rolled down the third inclined plane:
Acceleration= Vf - Vi/time Vf= d/t
A= 0.67 m/s - 0 m/s / 0.6 s Vf=0.4 m/0. 6 s
A= 1.11 m/s squared Vf= 0.67 m/s
Step 7 Mechanical Advantage of the Second Pulley System:
This next pulley system has 3 pulleys, therefore its mechanical advantage is 3.
Step 8 Mechanical Advantage of Pinwheel Lever:
The action of this step is the activation of a lever that contains a marble that will set off a chain reaction of collisions.
MA= force input/ force output
MA= 0.9 N/ 0.3 N
MA= 3
Step 9 Potential Energy of the Marble:
Before the marble collides with the dominoes, it has energy prior to its release:
Potential Energy= mass times acceleration due to gravity times height
PE= 0.0048 kg x 10 m/s squared x 0.1 m
PE= 0.0048 J
Step 10 Velocity of Spring Powered Car:
In the final step, a car hits the camera after it speeds down a track:
V= d/t
V= 0.52 m/ 0.41 sec
V= 1.27 m/s
Step 1 The Class Two Lever:
For the step that initiated the machine, we calculated the amount of work the lever did:
Work= Force times distance
W= 0.25 N x 13 cm
W= 3.25 J
Step 2 The Marble's Velocity:
As the marble rolled down the first inclined plane, we found it's velocity:
Velocity= distance/time
V=61 cm/0.62 sec
V=98.39 cm/sec or 0.98 m/sec
Step 3 Mechanical Advantage of the Second Inclined Plane:
Our first mechanical advantage calculation was for the second inclined plane:
Mechanical Advantage= input distance/output distance
MA= 34 cm/12 cm
MA= 2.83
Step 4 Mechanical Advantage of the Pulley System:
This step required no calculation, just simple knowledge of pulleys:
One pulley system has a mechanical advantage of 1.
Step 5 Force Exerted by the Wedge:
In this step, a golf ball is held in place by a simple machine called a wedge.
Force= mass times acceleration/mechanical advantage of ramp
F= 0.0475 kg x 10 m/s squared/ 10
F= 0.0475 N
Step 6 Acceleration of the Golf Ball:
For the sixth step, our calculation focused on the acceleration of the golf ball as it rolled down the third inclined plane:
Acceleration= Vf - Vi/time Vf= d/t
A= 0.67 m/s - 0 m/s / 0.6 s Vf=0.4 m/0. 6 s
A= 1.11 m/s squared Vf= 0.67 m/s
Step 7 Mechanical Advantage of the Second Pulley System:
This next pulley system has 3 pulleys, therefore its mechanical advantage is 3.
Step 8 Mechanical Advantage of Pinwheel Lever:
The action of this step is the activation of a lever that contains a marble that will set off a chain reaction of collisions.
MA= force input/ force output
MA= 0.9 N/ 0.3 N
MA= 3
Step 9 Potential Energy of the Marble:
Before the marble collides with the dominoes, it has energy prior to its release:
Potential Energy= mass times acceleration due to gravity times height
PE= 0.0048 kg x 10 m/s squared x 0.1 m
PE= 0.0048 J
Step 10 Velocity of Spring Powered Car:
In the final step, a car hits the camera after it speeds down a track:
V= d/t
V= 0.52 m/ 0.41 sec
V= 1.27 m/s