A loaded truck can accelerate at 4 m/s
2. It loses its load so that it is only 0.1 as massive.
By what factor must the acceleration
change for the same driving force?
To solve this problem, we can use the concept of Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration.
Let's assume the original mass of the loaded truck is M, and its acceleration is a. Therefore, according to Newton's second law, the force acting on the truck is given by F = M * a.
After losing its load, the mass of the truck becomes 0.1M (0.1 times the original mass), and we need to find the new acceleration, let's call it a'.
Since the driving force remains the same, we can equate the forces acting on the loaded truck and the unloaded truck:
F = F'
Using the formula for force, we have:
M * a = (0.1M) * a'
Simplifying the equation, we can cancel out the mass variable:
a = 0.1a'
To find the factor by which the acceleration must change, we can rearrange the equation:
a' = 10a
Therefore, the factor by which the acceleration must change is 10.
To calculate the factor by which the acceleration must change, we need to consider the relationship between force, mass, and acceleration described by Newton's second law of motion:
Force = mass x acceleration
The given information states that the loaded truck can accelerate at 4 m/s². Let's denote the mass of the loaded truck as M1 and the mass of the truck without its load as M2. The equation for the loaded truck can be written as:
Force1 = M1 x acceleration1
After the load is lost, the mass of the truck reduces to 0.1 times its original mass. Therefore, the mass of the truck without its load (M2) is:
M2 = 0.1 x M1
We want to determine the change in acceleration (let's call it acceleration2) needed for the same driving force. The equation for the unloaded truck can be written as:
Force2 = M2 x acceleration2
Since the force remains the same, we can equate the two equations:
Force1 = Force2
Which implies:
M1 x acceleration1 = M2 x acceleration2
Substituting the value of M2:
M1 x acceleration1 = (0.1 x M1) x acceleration2
Now, we can simplify the equation by canceling out the mass factor:
acceleration1 = 0.1 x acceleration2
To find the factor by which acceleration must change, we can divide acceleration2 by acceleration1:
factor = acceleration2 / acceleration1 = 1 / 0.1 = 10
Therefore, the acceleration must change by a factor of 10 for the same driving force when the truck loses its load.