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 calculate the change in acceleration when the truck becomes 0.9 times less massive.
Let's denote the initial mass of the loaded truck as m1 and the final mass after losing the load as m2. Additionally, denote the initial acceleration as a1 and the unknown final acceleration as a2.
According to Newton's second law of motion, force (F) is equal to mass (m) multiplied by acceleration (a): F = m * a. Since the driving force remains the same, we can equate the forces for both scenarios:
m1 * a1 = m2 * a2
We know that m2 = 0.9 * m1, so we can substitute this expression into the equation:
m1 * a1 = (0.9 * m1) * a2
Simplifying further:
a1 = 0.9 * a2
Now we need to determine the factor by which the acceleration must change, so divide both sides of the equation by a1:
a2 = a1 / 0.9
Therefore, the factor by which the acceleration must change is:
Factor = a2 / a1 = (a1 / 0.9) / a1 = 1 / 0.9 ≈ 1.11
Hence, the acceleration must increase by a factor of approximately 1.11 to achieve the same driving force when the truck becomes 0.9 times less massive.