A body was moving uniformly under the effect of three forces 𝐹 one, 𝐹 two, and 𝐹 three. Given that 𝐹 one equals seven 𝑖 and 𝐹 two equals eight 𝑗, where 𝑖 and 𝑗 are orthogonal unit vectors, determine 𝐹 three which ensures that it will move at a constant velocity.
We’re told in this statement two forces that are acting on a body, 𝐹 one and 𝐹 two, as well as their force descriptors. We want to solve for the value of the third force, 𝐹 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 𝐹 three, let’s recall Newton’s second law of motion. Newton’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, we’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 — 𝐹 one, 𝐹 two, and 𝐹 three — is equal to 𝑚 times 𝑎 which equals zero.
If we replace 𝐹 one and 𝐹 two with their component expressions and then subtract those components from both sides of our equation, we see that 𝐹 three equals negative seven 𝑖 minus eight 𝑗. That’s what 𝐹 three must be in order for the net force on our object to be zero.