Inclined Plane Black Line Drawing

This demonstration shows constant acceleration under the influence of gravity, reproducing Galileo's famous experiment. It can also be used in rotational dynamics [for a discussion on rotational dynamics, click here], to show and calculate moment of inertia, athwart velocity, athwart acceleration, and angular momentum.

This demonstration can also be used to show the static friction coefficients of different materials and how the force on an object will increment as the angle of the surface it lies on increases.

Listing of parts:

1. Painted black wooden ramp
2. Lab jack
3. Two sandbags
4. 50.8 mm diameter steel ball, mass 534.half dozen g
5. Two terminate clocks

Optional (to testify angle of aeroplane and related frictional effects)

1. Behemothic protractor
2. 2x modest clamps to attach protractor to slope
3. Plump bob/string (thin fishing line and 20g weight, found in blackboard mechanics)
4. Friction block with different surfaces

Caption:

Constant Acceleration:

To show abiding acceleration with this demo it tin can be a practiced to marking out distances on the ramp and then accept students time how long it takes for the ball to roll between the marks. They tin can use the time information technology takes for the ball to roll between the marks and from that calculate the acceleration at various different points on the ramp, which should all yield the same upshot (meaning the acceleration does not change with respect to fourth dimension).

To calculate the dispatch of the ball, yous can apply the equation a = (V₁ – 5_two)/t *. You will need to take viii dissimilar time measurements and will calculate four velocities and two accelerations. You can then compare the accelerations you calculate to see if the acceleration forth the ramp stays constant (which information technology should). To do this you volition desire to marking out eight evenly spaced marks on the ramp and take note of the fourth dimension that the brawl crosses each mark (Image of what the ramp should look like below)

What the ramp should await similar if marked for abiding acceleration demonstration, where the change in x should be equal beyond all 4 distances.

You can calculate Δt for each of the 4 segments of ramp with the equation:

Δt₁ = t₂ – t₁
Δt_ii = t₄ – t₃
And similarly for Δt₃ and Δt_iv

Δx is the distance between the marked points. Yous don't want them too long because you desire to get out time for the ball to accelerate between where you are calculating velocities, then they should be betwixt ten and 15 cm each. The altitude between the sets of marks does non make a deviation to the terminal calculations.

Because we know that V = Δt/Δx, nosotros tin can calculate the velocities across each distance Δx. This volition yield Five₁, V₂, Five_three, 5_four, which nosotros tin utilize to discover two accelerations, a_one, a_two. to notice the accelerations we use the equation:

a₁ = (V_i – V₂)/ t

where t for a₁, a₂ are t₄ and t₈, respectively.

From these calculations nosotros should discover that a_oneand a₂are equal (or nearly equal).

Friction:

This demo can also exist used to testify the relative static friction coefficients of unlike materials on forest. This demo is like to the static and kinetic friction demo, simply instead of changing the weight required to make the block motion, we can change the angle of the aeroplane. While the gravitational force acting on the block does not change depending on the angle of the board, a steeper incline volition requite a larger component force that is pushing the block down the ramp. This can be seen in the images below:

Equally seen above, a ramp with a larger θ (incline bending) will have a greater component force vector pushing it down the ramp (F₂), and a smaller component forcefulness vector that is pushing it directly into the ramp (F_ane). Because there is a greater force pulling the block downward the plane, a steeper incline will cause the block to brainstorm descending when it may non have on a shallower incline. It is important to notation here that the bending of the inclined plane volition exist the aforementioned every bit the angle betwixt the force of gravity and the force perpendicular into the plane. It is with this bending that we measure the component forces, F₁, and F₂.

The coefficient of static friction (μ) of the block on the ramp volition change magnitude of the strength (F₂) necessary to begin the block sliding. A greater μ volition require a greater force (and therefore a steeper incline) to begin moving than a smaller μ. [For a more in-depth discussion on how the coefficient of friction changes the force required to brainstorm moving an object, see the Static and Kinetic Friction demo,  here.]

A greater strength acting on the block can be created by increasing the angle (θ) of the ramp. This is because sin(θ) [when it is betwixt the values 0 and (π/2)] will increment with an increasing θ. So nosotros can hands seen that

If θ₁ > θ₂ so
F_yardsinθ₁ > F_grandsinθ_two

Every bit F₂ increases with increasing θ, it volition allow blocks with greater coefficients of static friction to begin to slide downward.

Notes:

• Make nigh a 10 cm height departure betwixt the ends of the ramp.
• It is a skillful idea to accept 2 students mensurate the travel time between marks on the ramp in order to calculate acceleration.

*This will have time and coordination so may non be viable to do in a big introductory physics class, but may be well suited to a easily-on outreach demonstration at a local high school or middle school.

Written by Sophia Sholtz

vegaboxistaken.blogspot.com

Source: https://ucscphysicsdemo.sites.ucsc.edu/physics-5a6a/ball-rolling-down-inclined-plane/

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