Introduction
In this video, we aim to calculate the static coefficient of friction for three different objects: an eraser, a candle, and a ruler. The experiment involves measuring two key distances, x and y, to derive the static coefficient of friction.
Key Measurements
- Distance x: Constant at 55.0 cm.
- Distance y: Varies based on the object and its placement on the plank. For the initial example, distance y is 29.9 cm.
Experiment Overview
- Objective: Determine the static coefficient of friction using the formula:
- Force of Friction = Static Coefficient of Friction (μ) × Normal Force. For a deeper understanding of normal force, check out our summary on Understanding Normal Force: A Comprehensive Guide.
- Understanding θ: The angle θ is defined as the angle between the plank and the tabletop. It can be calculated using:
- tan(θ) = Opposite / Adjacent = Distance y / Distance x
- Procedure:
- Slowly lift the plank until the object begins to move. Record the distance y at this point for each object (eraser, candle, ruler).
Force Diagram Explanation
- Forces Involved:
- Normal Force: Perpendicular to the plank.
- Force of Gravity: Acts downwards.
- Components of Gravity:
- Parallel to y-axis: F_g cos(θ) (adjacent over hypotenuse)
- Parallel to x-axis: F_g sin(θ) (opposite over hypotenuse)
Deriving the Formula
- At the point of sliding, the acceleration is zero, leading to balanced forces:
- Normal Force = F_g cos(θ)
- Force of Friction = F_g sin(θ)
- Substituting these into the friction formula shows that:
- Static Coefficient of Friction (μ) = tan(θ). For more insights on the relationship between normal force and weight, refer to Understanding Normal Force: Weight, Apparent Weight, and Scales.
Conclusion
The goal of the experiment is to complete the table with the calculated values for the static coefficient of friction for each object. This experiment can be replicated at home with simple materials. Have a great day!
good morning today our goal is to calculate the static coefficient of friction
for three different objects so to do this we'll have to measure two quantities
distance x and distance y as you can see from the diagram distance x and distance y are defined here
throughout this experiment distance x will be 55.0 centimeters this quantity will not change
distance y however will vary throughout the experiment distance y will depend upon the object
being used and where we place the object on the piece of wood
for this example distance y is 29.9 centimeters notice where distance y is measured
it's measured below the plank here is the table we're going to complete today we'll determine the style
coefficient of friction for an eraser candle and a ruler on a piece of wood so to determine the force of friction
it's given by the formula force of friction equals the static coefficient of friction
multiplied by the normal force this symbol is a greek letter it's mu and it stands for the static coefficient
of friction one can show that the static coefficient of friction
is equal to tan theta and so how is theta defined well going back to this diagram
theta is defined as the angle between the planck and the table top remember
tan theta is equal to the opposite side of the angle over the adjacent side with respect to the angle
and so for this situation tan theta is equal to opposite side distance y divided by
distance x the adjacent side so today to determine the static coefficient of friction
we'll be using the ratio of distance y to distance x so here's the experiment
i'm going to slowly lift the plank until the eraser begins to move as soon as i see it begin to move
right now and to stop lifting the plank please record that value for distance y
now i'm going to do this two more times again once i stop lifting the plank please
record the distance y value right around right around
now record that value notice i'm going very slowly it's important to lift the plank slowly
throughout this experiment here's the candle once again i'm lifting it very slowly
and the moment it begins to move i stop lifting it and you have to record the distance y
this is an experiment that you could certainly do at home you would just need to find a plank to
do this at home and here's the ruler there's the first distance y
second distance y and the final distance y now for those of you interested where we
get the formula mu equals tan theta or the static coefficient of friction equals tan theta i'm going to explain
that for you now this is the force diagram for any of the objects
friction opposes motion normal force is perpendicular to the plank and the force of gravity acts downwards
we're going to take the force of gravity and make a triangle with it in other words we're going to find the components
of the force of gravity that are parallel to the y-axis as defined in the diagram
and the x-axis notice that for the component of gravity that is parallel to the y-axis
we have the formula f g cosine theta it's cosine because it's adjacent over hypotenuse
notice for the component of gravity that is parallel to the x axis we have the formula fg sine theta sine
because it's opposite over hypotenuse just before the object begins to slide the acceleration is zero
so i was trying to mimic that in the experiment the moment i saw it slide i stopped lifting the plank so in theory
all of those distance y's are probably one or two millimeters less than the value we recorded
when the acceleration is zero we have two relations here in the y-axis we have that the normal
force is equal to the force of gravity times cosine theta for the x-axis we have that the force of
friction is equal to fg sine theta in other words everything has to be
balanced the forces have to be balanced when the acceleration is zero and that's what these two statements
here are saying now recall that the force of friction is
equal to the static coefficient of friction multiplied by the normal force
so if you wish you could substitute for the force of friction this expression f g sine theta
and for the normal force you can substitute f g cosine theta and one can show that the static
coefficient of friction is equal to tan theta so remember your goal today is to
complete the table have a great day bye-bye
The purpose of the experiment is to calculate the static coefficient of friction for three different objects: an eraser, a candle, and a ruler. This is achieved by measuring two key distances, x and y, and applying the relevant physics formulas.
The static coefficient of friction (μ) is calculated using the formula: μ = tan(θ), where θ is the angle between the plank and the tabletop. The angle θ can be determined by the ratio of distance y (the distance the object moves) to distance x (a constant distance of 55.0 cm).
The key measurements needed for the experiment are distance x, which is constant at 55.0 cm, and distance y, which varies based on the object being tested and its placement on the plank.
The forces involved in the experiment include the normal force, which acts perpendicular to the plank, and the force of gravity, which acts downwards. The components of gravity are also considered, with one component acting parallel to the y-axis and the other parallel to the x-axis.
Yes, the experiment can be easily replicated at home using simple materials. Viewers are encouraged to try measuring the static coefficient of friction for different objects using the outlined procedure.
The angle θ is significant because it directly influences the calculation of the static coefficient of friction. It is determined by the ratio of distance y to distance x, and it helps in understanding the balance of forces at the point of sliding.
For more insights on normal force, viewers can refer to the summaries linked in the video, such as "Understanding Normal Force: A Comprehensive Guide" and "Understanding Normal Force: Weight, Apparent Weight, and Scales." These resources provide a deeper understanding of the concepts involved.
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