an object is moving to the west at a constant speed. three forces are exerted on the object. one force is 10 n directed due north, and another is 10 n directed due west. what is the magnitude and direction of the third force if the object is to continue moving to the west at a constant speed?
What is the magnitude and direction of the third force if the object is to continue moving to the west at a constant speed?
Answer:
Given that the object is moving to the west at a constant speed and that two forces, 10 N directed due north and 10 N directed due west, are acting on the object, we can analyze the situation using vector addition. When the object is moving at a constant speed, the net force acting on it must be zero to maintain this motion.
Let’s denote the force directed due north as (\vec{F_1} = 10 N) in the positive y-direction, and the force directed due west as (\vec{F_2} = 10 N) in the negative x-direction.
To find the magnitude and direction of the third force ((\vec{F_3})), we need to ensure that the net force in the x-direction is zero because the object is moving to the west at a constant speed. This means the force in the positive x-direction (due east) must balance the force in the negative x-direction (due west).
Using vector addition, we find that (\vec{F_3} + (\vec{F_2}) = 0) for the object to move at a constant speed to the west.
(\vec{F_3} = -(\vec{F_2}) = -10 N)
So, the magnitude of the third force is 10 N, directed due east.
Therefore, the third force needed for the object to continue moving to the west at a constant speed is 10 N in the east direction.