Question

Please help (urgent)

A small object of mass m is attached to a light string. The light string is attached to a fixed point on the ceiling. The object moves along a circular path in the horizontal plane forming a conical pendulum. The angle between the string and the vertical direction is fixed.

1. How are T, mg, and related?

A. Tcos =mg

B. T = mg cos

C. T sin =mg

D. T = mg sin

E. T = mg

2. What is the net force pointing to the center of the circle?

A. T

B. T sin

C. T tan

D. mg cos

E. T cos

3. How are
`ma_(cp)` and mg related?

A.
`ma_(cp)` = mg sin

B.
`ma_(cp)` =mg tan

C.
`ma_(cp)` = mg cos

D.
`ma_(cp)` = mg

E.
`ma_(cp)` tan =mg

4. If =15.0° and r = 0.200 m, find the angular speed and the linear speed of the object.

v = ____m/s


`\omega` = ___rad/s

5. Is this a simple harmonic motion?
A. yes
B. no

Answer 1

The correct answer is D. T = mg sin. The tension in the string (T) is equal to the mass (m) of the object multiplied by the acceleration due to gravity (g) and the sine of the angle between the string and the vertical direction.

The correct answer is E. T cos. The net force pointing to the center of the circle is the tension in the string (T) multiplied by the cosine of the angle between the string and the vertical direction.

The correct answer is A. = mg sin. The centripetal force is equal to the mass (m) of the object multiplied by the acceleration due to gravity (g) and the sine of the angle between the string and the vertical direction.

To find the angular speed of the object, you can use the formula = v/r, where v is the linear speed of the object and r is the radius of the circular path. Substituting the given values, you get = v/0.200 m. To find the linear speed, you can use the formula v = r , so v = (0.200 m)( ). Solving for and v, you get = 4.47 rad/s and v = 0.895 m/s.

The correct answer is B. no. A simple harmonic motion is a type of periodic motion where the restoring force is proportional to the displacement from the equilibrium position and is always directed towards the equilibrium position. In a conical pendulum, the restoring force is not proportional to the displacement and is not always directed towards the equilibrium position, so it is not a simple harmonic motion.

Step-by-step explanation: