Video: Finding the Acceleration of a Body given the Force Vectors Acting on It

If a body of mass 1 kg moves under the action of forces ๐นโ‚ = (๐‘– + 8๐‘— โˆ’ 5๐‘˜) N and ๐นโ‚‚ = (2๐‘– โˆ’ 7๐‘— + 8๐‘˜) N, what is its acceleration?

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Video Transcript

If a body of mass one kilograms moves under the action of forces ๐น sub one equals ๐‘– plus eight ๐‘— minus five ๐‘˜ newtons and ๐น sub two equals two ๐‘– minus seven ๐‘— plus eight ๐‘˜ newtons, what is its acceleration?

Weโ€™ll refer to the mass of our body one kilogram as ๐‘š. And weโ€™re told the two forces ๐น one and ๐น two that are acting on the body. We want to solve for the bodyโ€™s resultant acceleration. Weโ€™ll call that ๐‘Ž. To solve for ๐‘Ž, letโ€™s start by recalling Newtonโ€™s second law of motion.

Newtonโ€™s second law tells us that the net force that acts on an object is equal to that objectโ€™s mass times its acceleration. So in our case, we can write ๐น one plus ๐น two equals ๐‘š times ๐‘Ž or ๐น one plus ๐น two all divided by ๐‘š equals ๐‘Ž. Since weโ€™re given ๐น one, ๐น two, and ๐‘š in our problem statement, we can plug in to solve for the acceleration.

In the numerator of our fraction, we have our two forces ๐น one and ๐น two being added together. When we combine them taking care to separate them out by ๐‘–, ๐‘—, and ๐‘˜ components, they result in three ๐‘– plus ๐‘— plus three ๐‘˜ newtons. Thatโ€™s the net force acting on our object.

And the mass of the object is one kilogram, which means that ๐‘Ž is equal to three ๐‘– plus ๐‘— plus three ๐‘˜ metres per second squared. Thatโ€™s the acceleration of our object under the influence of these two forces.

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