WEBVTT
00:00:00.720 --> 00:00:02.400
Two forces act on a particle.
00:00:03.120 --> 00:00:05.880
One of the forces has a magnitude of 14 newtons.
00:00:06.520 --> 00:00:08.600
But the magnitude of the other force is unknown.
00:00:09.880 --> 00:00:17.120
Given that the resultant force points in the direction of the angle bisector of the two forces, find the unknown magnitude.
00:00:18.400 --> 00:00:21.080
The problem can be modelled using the following diagram.
00:00:22.080 --> 00:00:25.040
Our two forces are 14 newtons and πΉ.
00:00:26.240 --> 00:00:27.800
The resultant force is labelled π
.
00:00:28.160 --> 00:00:39.200
As the resultant force points in the direction of the angle bisector of the two forces, the angle between the 14-newton force and π
is π.
00:00:40.440 --> 00:00:44.120
And the angle between π
and πΉ is also π.
00:00:45.520 --> 00:01:04.360
In order to solve the problem, we can use Lamiβs theorem, where each force is proportional to the sine of the angle between the other two forces, such that π΄ divided by sin πΌ is equal to π΅ divided by sin π½, which is also equal to πΆ divided by sin πΎ.
00:01:05.440 --> 00:01:26.320
In this case, 14 divided by sin π, the angle between π
and πΉ, is equal to πΉ divided by sin π, the angle between π
and 14 newtons, which is also equal to π
divided by sin two π, the angle between the 14-newton force and πΉ.
00:01:27.480 --> 00:01:36.240
As 14 divided by sin π is equal to πΉ divided by sin π, we can say that 14 is equal to πΉ.
00:01:37.600 --> 00:01:41.040
Therefore, the magnitude of the unknown force is 14 newtons.
00:01:41.760 --> 00:01:51.760
We can go one stage further here by saying that if the resultant force bisects any two forces, then the magnitude of those two forces must be equal.