How Do You Calculate the Velocity of a Compass Joint in Motion?

In summary, an engineering student is using a compass to draw on a drafting board. The compass has an arm length of 15 cm and initially has an angle of 60 degrees between the arms. As the student closes the compass at a speed of 0.060 m/s, the velocity of the joint can be calculated as a function of time. The velocity of the joint at the start and end of closing the compass can also be determined. The equations used for this calculation may involve the length of the arm, the position of the tips, and possibly unit vectors.
  • #1
scintillate10
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Homework Statement



An engineering student holds her open compass perpendicular to the drafting board, touching the board with both tips of the compass. She slowly closes the compass so that the tips move toward each other with a speed of 2 v_naught = 0.060 m/s. Initially the angle between the arms of the compass is 2theta=60 degrees. The arms of the compass are L = 15 cm long.

Calculate the velocity of the joint of the compass as a function of time.

AND Give the velocity of the joint at the moment that she starts to close the compass and at the moment that the two tips reach each other.

Homework Equations



I'm not sure but maybe L^2 = x^2 + y^2

or v = omega r


The Attempt at a Solution



I have no idea where to start this equation but the answer is really complex looking and involves a unit vector j . . .
 
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  • #2
I'm thinking it's something with the velocity of the joint and the angle of the compass somehow? I would really appreciate it if someone could help me out here. Thanks!
 

1. What is a related rates type physics problem?

A related rates type physics problem involves finding the rate of change of one quantity with respect to another quantity in a given scenario. This often involves using the chain rule to differentiate the related rates equation.

2. How do I approach solving a related rates type physics problem?

First, identify the quantities that are changing and their respective rates of change. Then, write an equation that relates these quantities. Use the chain rule to differentiate the equation and solve for the unknown rate of change.

3. What is the chain rule and how is it used in related rates type physics problems?

The chain rule is a calculus rule that is used to find the derivative of a composite function. In related rates type physics problems, it is used to differentiate the related rates equation and solve for the unknown rate of change.

4. Can you provide an example of a related rates type physics problem?

Sure, here's an example: A ladder is sliding down a wall at a rate of 2 feet per second. The base of the ladder is initially 6 feet away from the wall. How fast is the top of the ladder moving down the wall when the base is 8 feet away from the wall? In this problem, the rate of change of the top of the ladder sliding down the wall is the unknown rate that we need to find using the related rates equation.

5. Are there any tips for solving related rates type physics problems?

Yes, here are a few tips: 1) Draw a diagram to visualize the scenario and label the changing quantities. 2) Use the given information to write an equation that relates the changing quantities. 3) Differentiate the equation using the chain rule. 4) Substitute in the known values and solve for the unknown rate. 5) Don't forget to include units in your final answer.

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