Question

Tension on an Incline Plane

Set up your two masses as described at the beginning of the introduction of the lab, connected by a string across a pulley.

STEP 1: Calculate the coefficient of friction

Calculate the coefficient of kinetic friction (?_k) between the incline and m₁ friction by using the following method:

(1) Draw a picture of the apparatus that you used in the introduction.

We’ll be talking about forces. What characteristics of the apparatus do you think will be important in talking about forces? The length of the incline (D)? The mass of the block (m)? The acceleration due to gravity (g)? The angle of slope of the incline (q)? Draw or write any variables that you think may be important onto your picture.

Note: Do not use specific numbers. Use only variables at this stage. You may use paint to draw the picture and include it (by copy and paste) or just use words to explain.

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(2) Set up a coordinate system on your inclined plane and Draw a Free Body Diagram (FBD) of the block, with the forces, with directional arrows, acting on your block that you said were important from (1).

Hint: Your forces should include:

a) Normal force (N). How is the block supported as it sets on the incline? The board holds it up. The board must be exerting a force on the block to hold it up. This force is called the normal force. The direction of the normal force is straight up from the incline, so along the +y axis.

(b) Friction force (f ). Friction’s force has a direction exactly opposite the motion of the block. The block will move in the +x direction, so friction acts in the -x direction.

(c) Weight (mg). Gravity’s force is equal to mg. The direction of the force of gravity is straight down towards the center of the earth. Draw the x and y components of mg. Let the angle at the point mass be q (the same as the angle of incline).

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Now you should have all the forces. You can use Newton’s Second Law.

(3) Write equations using Newton’s Second Law, SF = ma, for each direction, x and y.

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(4) Calculate m_k in terms of q when the block is moving down the plane with constant speed. Given m₁= m₂

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(5) Find m_k. Suppose that the angle at which the block moves at constant speed is 20⁰, find m_k.

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STEP 2: Calculate the value of m₂ (the hanging mass)

Set the slope of the incline to 0°. Use Newton’s Second Law to predict how much mass needs to be strung over the pulley in order to make the block move with constant speed.

(a) Draw a picture of the setup and the Block’s FBD. Draw the appropriate coordinate system. Draw in m₁g, N, f, and the force due to the hanging mass, m₂g. In which direction does the force due to the hanging mass act? You may use paint to draw the picture and include it (by copy and paste) or just use words to explain.

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(b) Write equations for the x direction and the y direction using Newton’s Second Law. Think about accelerations. Predict what mass will pull the block along the incline at a constant speed.

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(c) Find the hanging mass (m₂) needed to pull the block along the board, inclined at 0°, at constant speed, given that m₁ is 245 gms.

STEP 3: Calculate m₂ for various angles

1) Choose 5 angles, 0º, 10º, 20º, 30º and 40º such that they are at least 10º apart from one-another.

For each for the situations,

Write all the forces acting on the masses,

Draw a free body diagram,

Calculate m₂ that must be hung from the pulley to make m₁ slide with constant velocity up the slope

2) Create a spreadsheet in excel.

Write the chosen angles in the first column.

In the second column write the predicted mass m₂ that must be hung from the pulley to make m₁ slide with constant velocity up the slope for each of your chosen angles. What formula will you be using to evaluate m₂?

Hint: Use the equation editor in excel rather than calculating each one by hand. It is a good idea to verify the answer by calculating it yourself in one of the cells to make sure you entered the equation in properly.

Answer 1