I did fine on kinematics, but circular motion has me a bit confused. There doesn't seem to be a concrete way of solving these questions. I know all the kinematic/dynamic formulas, but I have a hard time picking which one to use because every question is different, and each question requires picking a formula and changing it.
The other part is where we take something like;
Fc=T+Fg
then we change it to
Fc=T+mg
but it changes again if the object is at top or bottom like;
Fc=T-mg
it's all very confusing. I'm upgrading and this is the first time I've been in a classroom in over 5 years.
The other part is where we take something like;
Fc=T+Fg
then we change it to
Fc=T+mg
but it changes again if the object is at top or bottom like;
Fc=T-mg
it's all very confusing. I'm upgrading and this is the first time I've been in a classroom in over 5 years.
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Hi, Sam,
I'm guessing you're describing an object that's moving in a vertical circle, like a rock attached to a string. If that's the case, then
Fc = the centripetal force that accelerates the object toward the center of the circle
T = the tension in the string
±mg = the force due to gravity, where
m = the mass of the object, and
g = the acceleration of gravity, about 9.8 m/s²
If the object travels at a constant speed, then the magnitude of the acceleration, and therefore Fc, must be constant. If there were no gravity, then the tension in the string would also be constant. However, since gravity always pulls in one direction (namely, straight down), the tension in the string changes depending on whether gravity is "helping" or "fighting" the string.
When the object is at the top of the circle, then the tension in the string and gravity are working together to pull the object straight down. In other words, gravity is "helping" the string by pulling the object in the same direction, so their forces have the same sign: Fc = T + mg. The tension in the string is lower because gravity is doing part of the work.
When the object is at the bottom of the circle, then gravity is "fighting" the tension in the string: gravity is pulling the object down, while the string is pulling it straight up. Since the forces are pulling in opposite directions, they have opposite signs: Fc = T - mg. So, in order to keep the acceleration constant, the string must pull harder to compensate for gravity.
If you actually try the experiment by tying something heavy (but soft, just in case!) to a string, and then swinging it in a vertical circle, you can feel the object pulling harder when it's at the bottom than when it's at the top. The heavier the object, the greater the change in tension (because the "m" in "mg" is larger).
I hope that helps!
I'm guessing you're describing an object that's moving in a vertical circle, like a rock attached to a string. If that's the case, then
Fc = the centripetal force that accelerates the object toward the center of the circle
T = the tension in the string
±mg = the force due to gravity, where
m = the mass of the object, and
g = the acceleration of gravity, about 9.8 m/s²
If the object travels at a constant speed, then the magnitude of the acceleration, and therefore Fc, must be constant. If there were no gravity, then the tension in the string would also be constant. However, since gravity always pulls in one direction (namely, straight down), the tension in the string changes depending on whether gravity is "helping" or "fighting" the string.
When the object is at the top of the circle, then the tension in the string and gravity are working together to pull the object straight down. In other words, gravity is "helping" the string by pulling the object in the same direction, so their forces have the same sign: Fc = T + mg. The tension in the string is lower because gravity is doing part of the work.
When the object is at the bottom of the circle, then gravity is "fighting" the tension in the string: gravity is pulling the object down, while the string is pulling it straight up. Since the forces are pulling in opposite directions, they have opposite signs: Fc = T - mg. So, in order to keep the acceleration constant, the string must pull harder to compensate for gravity.
If you actually try the experiment by tying something heavy (but soft, just in case!) to a string, and then swinging it in a vertical circle, you can feel the object pulling harder when it's at the bottom than when it's at the top. The heavier the object, the greater the change in tension (because the "m" in "mg" is larger).
I hope that helps!