A horse pulls a barge down a canal. The horse pulls on the rope with a force of 7900 N at an angle of 18 degrees to the direction of motion of the barge, which is heading straigt along the canal. The mass of the barge is 9500kg and its acceleration is .12m/s^2. What are the a) magnitude and b) direction of the force on the barge from the water?
Would I use F=mg sin (theda)? How would I find the direction?
I would use the cosine function The direction has to be in the direction of the canal.
To find the magnitude of the force on the barge from the water, you can start by using Newton's second law of motion, which states that force equals mass times acceleration (F = ma). In this case, the mass of the barge is given as 9500 kg and the acceleration is given as 0.12 m/s^2. Therefore, the magnitude of the force on the barge is:
F = (9500 kg)(0.12 m/s^2) = 1140 N
Now, let's consider the direction of the force on the barge from the water. Since the horse is pulling on the rope at an angle of 18 degrees to the direction of motion of the barge, the force from the horse can be split into two components: one component parallel to the direction of motion, and one component perpendicular to the direction of motion.
To find the force component in the direction of motion, you can use the cosine function, as you correctly mentioned. The cosine of the angle (18 degrees) gives you the ratio of the force component parallel to the direction of motion to the total force applied by the horse. Therefore, you can calculate the force component in the direction of motion as:
Force in the direction of motion = (7900 N) * cos(18 degrees) = 7514 N
The force in the direction of motion is the force the horse applies to overcome any friction or resistance to motion in the canal.
Since the barge is heading straight along the canal, the force from the water has to counteract the force in the direction of motion. Therefore, the direction of the force on the barge from the water will be opposite to the direction of motion, which is the same as the direction of the force applied by the horse. So, the direction of the force from the water is 18 degrees relative to the canal.
In summary, a) the magnitude of the force on the barge from the water is 1140 N, and b) the direction of the force from the water is 18 degrees relative to the canal.