Physics concept problem?
I have the answer, I just don't understand it.
A girl swings a rock into a circular path while holding an attached spring overhead. The string makes a 45 degree angle to the vertical (comprising a conical pendulum). The centripetal force that holds the rock in its circular path is the
A) vertical component of the string tension
horizontal of the string tension
C) tension in the string
D) none of the above
The answer is B
Thanks
Update:These answers aren't helping...
Comments
Try to imagine a horizontal circle that is the path traced by the ball. As the ball is moving only in horizontal direction, its weight needs to be balanced by a vertical force, that comes from vertical component of spring tension (when object is placed on ground it is balanced by force by ground on object). And hence the horizontal component provides the necessary centripetal force required for circular motion.
The best way to picture this is with a picture, a so-called free-body diagram. But as Answers editing doesn't allow images, I draw one in our minds.
Looking at the whirling rock and string from the side, we see that the cord forms the hypotenuse of a right triangle with two 45 deg interior angles. We know there is tension, T, on the cord and that extends all the way to the rock. The other force is the rock's weight, W, which is straight down from the rock.
Now we break T and W into their XY components.
Tx = T cos(45) and Ty = T sin(45), these are just the two sides of the right triangle with T hypotenuse.
Wy = W and Wx = 0, weight is always in the vertical, never in the horizontal.
The rock is stable in its position at the end of the cord; it's not moving up/down or in/out while it whirls around that circle. So the forces listed above must be balanced, their sums must = 0. If there were a net non-zero force, the rock would be accelerating in the direction of that non-zero force. It isn't; so there is no net force.
Which means, ta da....
In the X direction, Tx + Wx = mV^2/R = T cos(45) which is the centripetal force pulling the rock of mass m towards the axis of rotation where V is the tangential speed of the rock around the radius of gyration R = L sin(45) where L is the length of the cord. ANS B. And now you know why.
Although you don't need this for this problem....
In the Y direction Ty - Wy = 0 so that T sin(45) = mg = W is the balance of forces that keeps the rock at the same height during the whirling.