A loaded truck can accelerate at 8.8 m/s
2
. It
loses its load so that it is only 0.6 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 first need to understand the relationship between acceleration, force, and mass.
Newton's second law of motion states that the force acting on an object is equal to the product of its mass and acceleration:
Force = mass × acceleration
In this scenario, the force acting on the truck remains constant. However, the mass of the truck changes, which means the acceleration must also change to keep the force constant.
Given that the loaded truck's mass is 1, and the mass of the truck after losing its load is 0.6, we can equate the forces in both scenarios:
Force (loaded truck) = mass (loaded truck) × acceleration (loaded truck)
Force (unloaded truck) = mass (unloaded truck) × acceleration (unloaded truck)
Since the force is constant, we can set these two equations equal to each other:
mass (loaded truck) × acceleration (loaded truck) = mass (unloaded truck) × acceleration (unloaded truck)
Now let's solve for the factor by which the acceleration must change:
acceleration (unloaded truck) = (mass (loaded truck) × acceleration (loaded truck)) / mass (unloaded truck)
Substituting the given values:
acceleration (unloaded truck) = (1 × 8.8) / 0.6
acceleration (unloaded truck) = 14.67 m/s^2
Therefore, the unloaded truck must have an acceleration of 14.67 m/s^2, which is approximately 1.67 times greater than the loaded truck's acceleration.
To summarize, the factor by which the acceleration must change for the same driving force is approximately 1.67.