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In this week’s lab we are going to examine
how acceleration is changed as we change both the force causing the
acceleration and the mass which is accelerated. Naturally if we
change both force and mass at the same time we will be unable to see how each
affects acceleration. So we shall modify them one at a time. |
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1. Assume we measure acceleration as we vary
force. If we plot force as our
independent variable (i.e. on the x axis) and acceleration as our dependent
variable (i.e. on the y axis) and knowing Newton’s second law? What is the slope of this graph? |
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Solve for a |
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Comparing
corresponding terms, we can see that |
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2. How do we find mass from this slope? |
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3. Assume we measure acceleration as we vary
the mass. If we plot mass as the
independent variable and acceleration as the dependent variable, and again
knowing Newton’s second law, what kind of curve will we get? |
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rewrite |
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to |
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Compare this to
the math equation |
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That is the equation for a Hyperbola! |
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OVER ŕ |
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4. Let’s consider the form of the equation
as |
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Now if we plot Ln(a)
on the independent axis (Y) and Ln(m) on the dependent axis (X), what should
our slope be? |
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Clearly our slope would be the power or (-1) |
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5. How would you determine the accelerating
force from the Ln(a)-Ln(m) plot? |
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We look at our
y-intercept which shows us |
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So the force is
found from |
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6. Suppose we have a mass that passes
through two photogates which are located a distance x apart, and each of
those photogates is capable of providing the speed of the mass as it passes
through the photogate, What expression would allow you to calculate the
acceleration of the mass? |
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We would have
two speeds, call them |
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Rearranging and
solving for a |
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