00:01
A ball of mass 0 .7 kilograms is tied to the end of a cord 0 .6 meters in length and is wound vertically to form an angle of 30 degrees below the horizontal.
00:10
Calculate the tension in the cord if the tangential velocity is 0 .7 meters per second.
00:17
So one tangential velocity at this angle of 30 degrees.
00:21
And we'll need one, the centrifugal force due to the rotational motion in the circular path called a fc.
00:39
And this tension force is counteracting that along with the components of the gravity, of the gravitational force, which is in this direction.
00:53
So we have to resolve that.
00:54
So this is fg.
00:58
And let's write the formula for the centrifugal force.
01:04
Fc is equal to fc is equal to mv squared over r.
01:17
The mass is equal to 0 .7 kilograms.
01:23
Velocity, the tangential velocity we're given as 0 .7 meters per second.
01:29
Square that divided by the radius, which is the length of the cord that is 0 .6 meters.
01:40
Let's leave that as it is for now.
01:42
And resolving this in this component, we're going to have a right angle triangle like this.
01:54
This is fg.
01:55
And this is fg, let's call it y.
02:05
This is going to be equal to the mass times the acceleration due to gravity.
02:09
This would be mg multiplied by our angle here.
02:14
So this is the opposite side.
02:17
So we have sine here.
02:18
This is the adjacent side...