Inclined Planes
Introduction:
One of the earliest machines man used was the inclined plane. An inclined plane is simply a tilted surface. We use inclined planes frequently. Ramps and even flights of stairs are inclined planes. Remember that Work = Force x distance and that when we use simple machines like an inclined plane we will have two forms of work:
Work input (W in
) = F e
x d e
is the work done by you; and
Work output (W out
) = F r
x d r
is the work done to the object.
LAB # 5-3 Inclined Planes
MATERIALS : 1 m board, string, textbook, spring scale, ring stand, clamp, meter stick
PURPOSE : In this investigation you will use an inclined plane to measure and compare W in and W out
. You will also discover how the slope of an incline plane affects its efficiency.
After completing this investigation you will also be able to:

Calculate work

Measure forces

Calculate the efficiency of a machine
HYPOTHESIS : Which will provide better efficiency in an inclined plane, a steeper slope or a gradual slope?
PROCEDURES:
PROCEDURE: Part 1 – Work Input vs. Work Output
1.
Make a loop of string to serve as a handle and loop it around the binding of a book.
2.
Clamp one end of the 1 meter board to the ring stand clamp and raise it on the ring stand until the bottom edge of the board reaches a height of 0.1 m and tighten the clamp. You will use this inclined plane to do work. Note that the length of the board is the effort distance (the distance you will move) and is recorded as effort distance in Data Table 1.
3.
Place the book at the end of the inclined board and attach a spring scale to the string loop.
While one partner holds the board, the other partner should slide the book up the incline and observe the effort force (F e
) needed to keep the book moving (Do not measure the force needed to start the book in motion.) Record this as Effort Force in Data Table 1.
Note: Pull the scale parallel to the board, not at an angle above it. See Figure 1.
4.
Raise the board to each of the other incline heights listed in Data Table 1.
At each height, slide the book up the incline and record the average effort force. (Note that when the height of the incline is above the height of the ring stand, clamp the side of the board and support the other
Figure 1 side with your hand.)
5.
The load (resistance force) moved up the incline plane is the weight of the book. Weigh the
0.1 m book with the spring scale and record this weight for each trial as the resistance force in Data
Table 2.
6.
The height the book is moved by the machine is the height of the incline. These heights have been recorded as the resistance distance for each trial in Data Table 2.
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5
6
2
3
4
Trial
7.
Use the formula given in the introduction to calculate Work Input and Work Output for each trial and record them in Data Tables 1 & 2.
8.
Calculate the ideal mechanical advantage using the formula MA = l
/h for each trial and record in Data Table 2.
9.
Calculate the actual mechanical advantage using the formula MA = F r
/F e
for each trial and record in Data Table 2.
DATA TABLE 1 : Work Input DATA TABLE 2: Work Output and MA
Incline
Height
Effort
Force
(F e
)
Effort
Distance
(d e or l)
Work
Input
(W in
)
Trial
Incline
Height
Resistance
Force
(F r
)
Resistance
Distance
(d r
)
Work
Output
(W out
)
Ideal
MA
Actual
MA
1 0.1 m ___N 1.0 m ____Nm 1 0.1 m ___N 0.1 m ____Nm
0.2 m ___N 1.0 m ____Nm
0.3 m ___N 1.0 m ____Nm
0.4 m ___N 1.0 m ____Nm
0.5 m ___N 1.0 m ____Nm
2
3
4
5
0.2 m
0.3 m
0.4 m
0.5 m
___N
___N
___N
___N
0.2 m
0.3 m
0.4 m
0.5 m
____Nm
____Nm
____Nm
____Nm
0.6 m __N 1.0 m ____Nm 6 0.6 m __N 0.6 m ____Nm
.
Efficiency
The ratio of Work output to Work input is called efficiency. This ratio is usually expressed as a percentage. The efficiency of the incline plane can be computed as follows:
Efficiency = W out
x 100 = ____________%
W in
As you can see, the “efficiency” indicates the amount of input work which is converted to output work.
PROCEDURE: Part 2 – Efficiency
1.
Use the values you calculated for W in
and W out
in Part 1 to compute the efficiency of the inclined plane at each of the trial heights. Record these answers in Data Table 3.
DATA TABLE 3 – Efficiency
Trial
Incline
Height
(m)
Efficiency
%
1
2
3
0.1 m
0.2 m
0.3 m
________%
________%
________%
4
5
6
0.4 m
0.5 m
0.6 m
________%
________%
________%
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QUESTIONS:
1.
Compare the values of W in
and W out
in Data Tables 1 & 2. a. W in
> W out b. W in
< W out c. W in
= W out
2.
Do you get as much work out of an inclined plane as you put into it?
3.
Explain your answer to number 2.
4.
If W in
is always greater than W out
, in what way does the inclined plane help you do work?
5.
As the height of the inclined plane increases, the efficiency of the inclined plane _________. a. decreases b. increases c. stay the same
6.
Why is the efficiency of a simple machine always less than 100%?
7.
Contrast the Ideal MA (d e
/d r
) to the Actual MA (F r
/F e
). Why is there such a difference between the two?
8.
A box weighs 280 N and is pushed up a 2 m inclined plane. The box is pushed with an effort force of 150 N. If the box is raised to a height of 1 m, find the efficiency of the inclined plane.
Extra Credit Questions – You must show all your work to gain credit
9.
Find the effort force required to raise a 1200 N parcel 1 meter if you use a 5 m long inclined plane which has an efficiency of 50%.
10.
You need to move a 2000 N appliance up a 4 m inclined plane to a truck bed that is 1 m off the ground. The efficiency of the inclined plane and cart is 80%. If your maximum possible effort force is 600 N, can you do this job by yourself or do you need to call your friend?
Show your work to prove your answer.
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