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Current time:0:00Total duration:2:59

Identifying force vectors for pendulum: Worked example

AP.PHYS:
INT‑3.B (EU)
,
INT‑3.B.2 (EK)
,
INT‑3.B.2.1 (LO)

Video transcript

we're told that a ball attached to a string swings in a horizontal circle at constant speed as shown below the string makes an angle theta with the horizontal which arrows show all the forces on the ball so pause this video and see if you can figure that out okay so let's work through this together so this ball is attached to the string and it's clearly hanging down and I think it's fish it's fair to say that we are on some type of a planet and so if we're on some type of a planet you're definitely gonna have the force of gravity acting on the ball so let me draw that vector so the force of gravity I'll do an orange let's say it looks something like that it's a magnitude I'll denote as capital F with a sub G right over here now what's keeping that ball from accelerating downwards and also what's keeping that ball in this uniform circular motion and the answer to both of those questions is the tension in the rope remember tension is a pulling force the Rope is pulling on this ball and so we could say the force of the tension so it might look something like this the force force of the tension now just with that we have constructed a Freebody diagram and we can immediately answer their question what are the forces that are acting on the ball which arrows show it so there's one downward and then there's one going in the direction of the string and if you look at these choices here you would say it is that one right over there now some of you might be saying wait hold on a second isn't there some type of a centripetal force that keeps the ball going in a circle that keeps it from just going straight away straight off and then isn't there some type of force that counteracts the actual force of gravity and the answer the question is yes there is but those are really just components of the tension and so if you look at the X component of the tension I'll do that in a blue color right over here this X component of the tension so I'll call that F sub T X that is our centripetal force or that's magnitude of the X component of tension is the same thing as the magnitude of our centripetal force and if we look at if we look at the y component of our attention the y component of our tension that's what counteracts the force of gravity so this right over here it's magnitude is F sub T y and F sub T Y this magnitude is going to be the same thing as the magnitude of the force of gravity but we already answered our question and we just got a little bit more intuition of what's going on right over here