Question

what is the formula for conical pendulam​

Answer 1

Answer:

This is called a centripetal force. The equation for centripetal force is Fc = mv 2 /r, where m is the mass of the object, v is the tangential velocity, and r is the radius of the circular path.

Answer 2

Explanation:

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The tension in the string pulls the plane up and in. The horizontal component of the tension pulls the plane toward the center of the circle, causing the plane to move in a circular path. This is called a centripetal force. The equation for centripetal force is Fc = mv 2 /r, where m is the mass of the object, v is the tangential velocity, and r is the radius of the circular path.

Part III: Calculate the Theoretical Speed of the Plane Using Forces and the Laws of Motion

Conical Pendulum Figure 3Carolina

Step 1: In the space below, draw a free body diagram of the forces acting on the plane while it is in flight.

T = tension

m = mass

g = acceleration due to gravity (9.8 m/s2 )

(The force from the propeller is directed in or out of the page, depending on which way the plane is flying.)

Step 2: Resolve the components of the forces from the diagram in Step 1 to horizontal and vertical components, and find a mathematical expression for these components in terms of the forces in Step 1.

Conical Pendulum Figure 4Carolina

Tx = horizontal component of tension

Ty = vertical component of tension

Conical Pendulum Figure 5Carolina

Step 3: Set the horizontal component of the tension equal to the centripetal force causing the plane to move in a circle.

Conical Pendulum Figure 6Carolina

Step 4: Solve this equation for velocity.

Conical Pendulum Figure 7Carolina

Here, v is the magnitude of the tangential velocity of the plane, or the speed.

Step 5: Find θ by measuring the length of the string (from the pivot point to the center of the plane) and the radius (follow the procedure in Part II, Step 1).

Conical Pendulum Figure 8Carolina

L = length of the string (meters)

r = radius of the circular path (meters)

θ = angle between the string and the vertical (degrees)

Conical Pendulum Figure 9Carolina

Record your measurements here:

r = ______________ (meters)

L = __________________ (meters)

sinθ = _______________

θ = __________________ (degrees)

Step 6: Substitute the value for θ from Step 5 into the equation for velocity from Step 4 and solve for the velocity of the plane.

Step 7: Compare the value given by the calculation in Step 6 with the value measured in Part II. Calculate the percent difference in the 2 values. Are the values the same? What are the sources of error in the calculations?

Sources in error include human error while measuring the length of the string, the radius of the circle, and the measurement of the period of revolution. The plane is a fairly large pendulum bob. Finding the exact point from which to measure the radius using a laser pointer is a likely source of error.

Conical Pendulum Figure 10Carolina

Answer the following questions from Part III:

1. Based on the free body diagram you drew, explain the motion of the plane. Why does the plane move in a horizontal circle, and why doesn’t the plane move up and down?

The forces on the plane in the vertical direction are balanced so the plane does not move up and down. The horizontal component of the tension is not balanced and always points toward the center of the circle, while the thrust from the plane’s propeller is always directed tangent to the plane’s circular path.

2. Is it necessary to measure the mass of the plane?

(Hint: See Part III, Step 3.)

The mass of the plane cancels out when you set the equation for centripetal force equal to the horizontal component of the tension. It is not necessary to measure the mass of the plane.