A truck of mass M is moving under a force F with acceleration a. If the truck is then loaded with an object of mass equal to the mass of the truck and the driving force is halved, then what is the new acceleration?
Question
A truck of mass M is moving under a force F with acceleration a. If the truck is then loaded with an object of mass equal to the mass of the truck and the driving force is halved, then what is the new acceleration?
Solution
Sure, let's solve this step by step.
Step 1: Understand the initial situation The truck of mass M is moving under a force F with acceleration a. According to Newton's second law of motion, F = Ma.
Step 2: Understand the changes The truck is then loaded with an object of mass equal to the mass of the truck, so the total mass becomes 2M. The driving force is halved, so the new force becomes F/2.
Step 3: Apply the changes to the formula We need to find the new acceleration, let's call it a'. According to Newton's second law of motion, the force equals the mass times the acceleration. So, F/2 = 2M * a'.
Step 4: Solve for the new acceleration To solve for a', we divide both sides of the equation by 2M. So, a' = (F/2) / (2M) = F / (4M).
So, the new acceleration of the truck is a quarter of the original acceleration.
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