A force of 100 N is acting at a point Resolve this force along 300 and 400
To resolve a force into its components, we need to find the projection of the force onto each of the given directions. In this case, we have a force of 100 N and two directions, 300 and 400.
To resolve the force along the direction of 300, we need to find the projection of the force onto this direction. The projection of a force F onto a direction vector D is given by the formula:
Magnitude of the projection = (Magnitude of F) * (Cosine of the angle between the force and the direction)
First, we need to find the angle between the force and the direction vector. To do this, we can use the dot product of the force and the direction vector:
Angle = arccos((Force dot Direction) / (Magnitude of Force * Magnitude of Direction))
Let's calculate this:
Magnitude of the force = 100 N
Magnitude of the direction = 300
Force dot Direction = 100 * 300 = 30000
Magnitude of Force * Magnitude of Direction = 100 * 300 = 30000
Angle = arccos(30000 / 30000) = arccos(1) = 0 radians
Since the angle between the force and the direction vector is 0 radians, the force is already aligned with the direction vector. Therefore, the magnitude of the projection of the force along the direction of 300 is equal to the magnitude of the force itself:
Magnitude of the projection along 300 = 100 N
Similarly, the magnitude of the projection of the force along the direction of 400 can be calculated using the same method:
Magnitude of the direction = 400
Force dot Direction = 100 * 400 = 40000
Magnitude of Force * Magnitude of Direction = 100 * 400 = 40000
Angle = arccos(40000 / 40000) = arccos(1) = 0 radians
Again, since the angle between the force and the direction vector is 0 radians, the force is already aligned with the direction vector. Therefore, the magnitude of the projection of the force along the direction of 400 is equal to the magnitude of the force itself:
Magnitude of the projection along 400 = 100 N
Hence, the force of 100 N can be resolved to 100 N along the direction of 300 and 100 N along the direction of 400.