Question Video: Finding Unknown Components of Force Acting on a Body Moving Uniformly Where Two Other Forces Are Acting on It | Nagwa Question Video: Finding Unknown Components of Force Acting on a Body Moving Uniformly Where Two Other Forces Are Acting on It | Nagwa

# Question Video: Finding Unknown Components of Force Acting on a Body Moving Uniformly Where Two Other Forces Are Acting on It Mathematics • Third Year of Secondary School

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A body was moving uniformly under the effect of three forces ๐นโ, ๐นโ, and ๐นโ. Given that ๐นโ = 7๐ and ๐นโ = 8๐, where ๐ and ๐ are orthogonal unit vectors, determine ๐นโ which ensures that it will move at a constant velocity.

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### Video Transcript

A body was moving uniformly under the effect of three forces ๐น one, ๐น two, and ๐น three. Given that ๐น one equals seven ๐ and ๐น two equals eight ๐, where ๐ and ๐ are orthogonal unit vectors, determine ๐น three which ensures that it will move at a constant velocity.

Weโre told in this statement two forces that are acting on a body, ๐น one and ๐น two, as well as their force descriptors. We want to solve for the value of the third force, ๐น three, which ensures that, overall, the body will move at a constant velocity. In other words, that its acceleration will be zero.

To start solving for ๐น three, letโs recall Newtonโs second law of motion. Newtonโs second law says that the net force acting on an object is equal to the mass of that object times its acceleration. In our scenario, weโre told the object moves at a constant velocity. That means that its acceleration is zero. So we can write, the sum of our three forces โ ๐น one, ๐น two, and ๐น three โ is equal to ๐ times ๐ which equals zero.

If we replace ๐น one and ๐น two with their component expressions and then subtract those components from both sides of our equation, we see that ๐น three equals negative seven ๐ minus eight ๐. Thatโs what ๐น three must be in order for the net force on our object to be zero.

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