How Do Components of Force Affect Barge Movement in Vector Addition?

[Gughanath]

a horse pulls a barge along a canal using a rope 10m long. if the barge is 2m from the bank, the rope is taught and the tension in it is 500N. what are the components of this force at right angles to the canal?
i worked this out to be 99.7N i used 500 x sin 11.5 (the angle between the rope and the bank)

 

[Fredrik]

The result should be 100 N. (It has to be one fifth of the force in the direction of the rope, because the distance from the bank is one fifth of the length of the rope). If you get 97.5 N it must be because of a roundoff error. The angle isn't exactly 11.5.

 

[wais]

Your calculation is correct. The components of the force at right angles to the canal are 99.7N, which is the force pulling the barge towards the bank, and 500N, which is the force keeping the barge from moving away from the bank. This is an important concept in vector addition, where the total force is the combination of both magnitude and direction of the individual forces. In this case, the horse is pulling with a force of 500N along the rope, but due to the angle between the rope and the bank, only a component of that force is actually pulling the barge towards the bank. This is why it is important to consider both magnitude and direction when adding vectors.