A loaded truck can accelerate at 6.4 m/s^2. It loses its load so that it is only 0.9 as massive. By what factor must the acceleration change for the same driving force?
To find the factor by which the acceleration must change, we need to understand the relationship between acceleration, mass, and force. According to Newton's second law of motion, the force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, this can be represented as:
Force = Mass × Acceleration
Given that the initial acceleration (a1) is 6.4 m/s^2 and the initial mass (m1) is the actual mass of the loaded truck, and the final mass (m2) is only 0.9 times the actual mass, we can calculate the factor by which the acceleration must change to maintain the same driving force (F) using the following steps:
Step 1: Calculate the initial force (F1):
F1 = m1 × a1
Step 2: Calculate the final force (F2), using the same driving force:
F2 = m2 × a2
Since F1 = F2 (same driving force), we can set the two equations equal to each other:
m1 × a1 = m2 × a2
Step 3: Substitute m2 = 0.9 × m1 into the equation:
m1 × a1 = (0.9 × m1) × a2
Step 4: Simplify the equation by dividing both sides by m1:
a1 = 0.9 × a2
Now we can determine the factor by which the acceleration must change:
Factor = a2 / a1
Since a1 = 6.4 m/s^2, we can substitute it into the equation:
Factor = a2 / 6.4
Therefore, to find the factor by which the acceleration must change, we need to know the value of a2, the new acceleration.