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. Another is 10 N directed due west. What is the magnitude and direction of the 3rd force if the object continues moving west at constant speed? Please explain and draw a force diagram.
A. 10 sqrt(3) N northwest
B. 10 sqrt(3) N southeast
C. 10 sqrt(2) N northwest
D. 10 sqrt(2) N southeast
To solve this problem, we need to use the concept of vector addition and the principle of equilibrium for constant velocity motion.
Given:
Since the object is moving at a constant speed to the west, the net force acting on it must be in the westward direction. This means that the vector sum of all the forces acting on the object must be directed towards the west.
We need to find the third force (Force 3) such that the vector sum of all three forces is directed towards the west.
To find the direction of Force 3, we can use the vector addition method. We first add Force 1 and Force 2 to find the resultant vector, and then Force 3 should be equal in magnitude but opposite in direction to the resultant vector.
The resultant vector of Force 1 and Force 2 can be calculated using the Pythagorean theorem:
Magnitude of the resultant vector = √(10^2 + 10^2) = 10√2 N
The direction of the resultant vector is tan^-1 (10/10) = 45° from the positive x-axis (northwest direction).
Therefore, Force 3 should be directed towards the southeast, with a magnitude of 10√2 N, to counteract the resultant vector and maintain constant velocity towards the west.
The correct answer is D. 10√2 N southeast.