How does trigonometry help determine the gravity component on an inclined plane?

In summary: Substituting in g/sin60 for g into that equation and getting D, but the answer should be C.Look at it this way. Which of the choices (1) depends on the angle and gives the expected answer when the angle of the incline is, instead of 60o, (2) 90o and (3) 0o ?Since the plane is frictionless, only the component of gravity along the plane matters, which is gsin60. It is then identical to the case of a simple pendulum where g is replaced by g sin60
  • #1
jaewonjung
9
0
Homework Statement
Question is in the file.
Relevant Equations
T=2pi root(l/g)
Since gravity is acting downward, I found the gravity component parallel to the plane, which was g/sin60.
I substituted g/sin60 for g into that equation and got D, but the answer should be C.
 

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  • #2
Look at it this way. Which of the choices (1) depends on the angle and gives the expected answer when the angle of the incline is, instead of 60o, (2) 90o and (3) 0o ?
 
  • #3
kuruman said:
Look at it this way. Which of the choices (1) depends on the angle and gives the expected answer when the angle of the incline is, instead of 60o, (2) 90o and (3) 0o ?
Well, I know that A is wrong since it is independent of the angle. The other answer choices have an angle component.
 
  • #4
In these sorts of MCQs, it saves time to think of the extremes - what happens if the plane were absolutely horizontal or completely vertical? What would the period be in those cases? Which of of the choices make sense in that light? You'll have your answer.
 
  • #5
hurreechunder said:
In these sorts of MCQs, it saves time to think of the extremes - what happens if the plane were absolutely horizontal or completely vertical? What would the period be in those cases? Which of of the choices make sense in that light? You'll have your answer.
Thanks for the reply!

I see. If the angle was approaching 0, the period would approach infinity, since the pendulum would almost be completely horizontal and gravity would have a negligible effect. I understand why C is the answer and not D, but I still don't understand how to algebraically find the equation for the period.
 
  • #6
Since the plane is frictionless, only the component of gravity along the plane matters, which is gsin60. It is then identical to the case of a simple pendulum where g is replaced by g sin60
 
  • #7
I found the gravity component parallel to the plane, which was g/sin60.
Review your trigonometry that lead you to that conclusion.
 

Related to How does trigonometry help determine the gravity component on an inclined plane?

1. What is a pendulum on an inclined plane?

A pendulum on an inclined plane is a simple physical system that consists of a pendulum hanging from a string or rod attached to an inclined surface.

2. How does a pendulum on an inclined plane work?

A pendulum on an inclined plane works by utilizing the force of gravity and the law of conservation of energy. As the pendulum moves along the inclined plane, it converts potential energy into kinetic energy and back again, creating a back-and-forth motion.

3. What factors affect the motion of a pendulum on an inclined plane?

The motion of a pendulum on an inclined plane is affected by the angle of the incline, the length of the pendulum, and the force of gravity. These factors determine the speed, period, and amplitude of the pendulum's motion.

4. What is the relationship between the angle of the incline and the motion of the pendulum?

The angle of the incline has a direct impact on the motion of the pendulum. As the angle increases, the force of gravity acting on the pendulum increases, resulting in a higher speed and shorter period of motion. As the angle decreases, the opposite occurs.

5. What are some real-world applications of a pendulum on an inclined plane?

Pendulums on inclined planes have various practical uses, such as in clocks and metronomes to keep time, in earthquake seismometers to measure ground vibrations, and in amusement park rides. They are also commonly used in physics experiments to demonstrate principles of energy and motion.

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