two crewman pull a boat through a lock, one with a force of 135N at an angle of 37 degrees relative to the forward direction of the raft. The 2nd crewman on the opposite side of the lock pulls at an angle of 45 degrees, with what force should the 2nd crewman pull so that the net force of the two crewman is in the forward direction
side force port = 135 sin 37
side force starboard = F sin 45
so
F = 135 (sin 37 / sin 45)
for no net force to either side
To determine the force at which the second crew member should pull in order for the net force to be in the forward direction, we need to break down the forces exerted by each crew member and analyze their horizontal and vertical components separately.
Let's denote the force exerted by the first crew member as F1 and the force exerted by the second crew member as F2.
First, let's find the horizontal and vertical components of F1:
Horizontal component of F1 = F1 * cos(37°)
Vertical component of F1 = F1 * sin(37°)
Similarly, let's find the horizontal and vertical components of F2:
Horizontal component of F2 = F2 * cos(45°)
Vertical component of F2 = F2 * sin(45°)
Now, since we want the net force to be in the forward direction, the vertical components of the two forces should cancel each other out:
Vertical component of F1 + Vertical component of F2 = 0
Substituting the respective components, we have:
F1 * sin(37°) + F2 * sin(45°) = 0
Simplifying the equation, we get:
F1 * sin(37°) = -F2 * sin(45°)
(Note: We multiply F2 by -1 since the vertical component of F2 is in the opposite direction of F1.)
Now, to find the force F2, we can rearrange the equation:
F2 = -F1 * sin(37°) / sin(45°)
Substituting the given value of F1 (135N), we can calculate F2:
F2 = -135 * sin(37°) / sin(45°)
Calculating this expression, we find that F2 is approximately -130.03N. Since the magnitude of a force cannot be negative, the positive value of F2 is 130.03N.
Therefore, the second crew member should pull with a force of approximately 130.03N at an angle of 45 degrees relative to the forward direction in order for the net force of the two crew members to be in the forward direction.