If a loaded truck that can accelerate at 1 m/s2 loses its load and has one-half of the original mass, what acceleration can it attain from the same driving force?
F = m a so a = F/m
same F, m' = m/2
F = (m')a'
a' = F/m' = F/(m/2) = 2 F/m = 2 a
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To find out the acceleration that the loaded truck can attain after losing its load and having one-half of the original mass, we need to understand the concept of Newton's second law of motion.
Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be represented by the equation:
F = ma
Where F is the net force acting on the object, m is its mass, and a is its acceleration.
In this scenario, we are told that the truck can accelerate at 1 m/s² with its original mass. Let's assume the original mass is 'm'. So the net force acting on the truck can be calculated as:
F = m * a
Now, when the truck loses its load, it has one-half of the original mass, which is (1/2) * m.
Let's calculate the new acceleration (a') using the same net force and the new mass:
F = (1/2) * m * a'
By comparing the two equations for the net force, we can equate them:
m * a = (1/2) * m * a'
Now, we can divide both sides of the equation by m:
a = (1/2) * a'
Next, we can isolate 'a' on one side of the equation:
a' = 2 * a
Therefore, the acceleration that the loaded truck can attain after losing its load and having one-half of the original mass will be twice the original acceleration. Thus, the new acceleration is 2 m/s².