If a body of mass one kilograms moves under the action of forces 𝐹 sub one equals 𝑖 plus eight 𝑗 minus five 𝑘 newtons and 𝐹 sub two equals two 𝑖 minus seven 𝑗 plus eight 𝑘 newtons, what is its acceleration?
We’ll refer to the mass of our body one kilogram as 𝑚. And we’re told the two forces 𝐹 one and 𝐹 two that are acting on the body. We want to solve for the body’s resultant acceleration. We’ll call that 𝑎. To solve for 𝑎, let’s start by recalling Newton’s second law of motion.
Newton’s second law tells us that the net force that acts on an object is equal to that object’s mass times its acceleration. So in our case, we can write 𝐹 one plus 𝐹 two equals 𝑚 times 𝑎 or 𝐹 one plus 𝐹 two all divided by 𝑚 equals 𝑎. Since we’re given 𝐹 one, 𝐹 two, and 𝑚 in our problem statement, we can plug in to solve for the acceleration.
In the numerator of our fraction, we have our two forces 𝐹 one and 𝐹 two being added together. When we combine them taking care to separate them out by 𝑖, 𝑗, and 𝑘 components, they result in three 𝑖 plus 𝑗 plus three 𝑘 newtons. That’s the net force acting on our object.
And the mass of the object is one kilogram, which means that 𝑎 is equal to three 𝑖 plus 𝑗 plus three 𝑘 metres per second squared. That’s the acceleration of our object under the influence of these two forces.