Forces on an Incline

Theory

The weight of any object on an incline is decomposed into its parallel and perpendicular components. The parallel one, unless equilibrated by another force F, causes the down-the-hill acceleration. The perpendicular one is equilibrated by the normal force; hence, there is no motion in the perpendicular direction.

Experimental Procedure

Objectives

The objective of this lab is to investigate the parallel component of the weight of an object placed on an inclined plane as a function of the angle of the inclination.

Research Question: How is the force directed parallel to the inclined plane related to the weight of an object?

Laboratory Settings

On the table, you will find an inclined plane, a cart, weights, and a force sensor. Set the inclined plane as shown in the diagram on your lab worksheet.

Make sure to secure the stand with a C-clamp.
Set the force sensor to the range of 50 N.
Be careful with the weights so they do not drop on your foot.

Find a method of measuring the angle of inclination.

In the figure below, a method of measuring both sine and cosine of the angle is shown. Depending on your design, you may want to use either the angle θ or its function, e.g. sin θ (see calculations below)

an inclined plane with rulers placed to measure the hypotenuse, adjacent, and opposite sides of a triangle

sin θ = opposite/hypotenuse

sin θ = 6 cm / 50.4 cm = 0.119

arc sin 0.12 = 6.837 ~ 7°

cos θ = adjacent/hypotenuse

cos θ = 50.0 cm / 50.4 cm = 0.992

arc cos 0.99 = 7.22 ~ 7°

tan θ = opposite/adjacent

tan θ = 6 cm / 50 cm = 0.120

arc tan 0.120 = 6.843 ~ 7°

Here are some examples of measuring the angle with a ruler in the lab. Remember to measure the hypotenuse from that end of the incline that touches the table.

an example of measuring angles with a ruler

another example of measuring angles with rulers

Data Collection and Analysis

Measure the parallel component of the weight for several different angles.

Collect the data in the table in your lab worksheet.
Plot the data points.
Create a graph of the investigated force as a function of the angle of inclination.

Do the plotted points form any shape known from your precalc class? According to the theory, what mathematical function can be used to model the plotted points? Why?

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