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 find the factor by which the acceleration must change, let's first understand the relationship between acceleration, mass, and force.
The formula to calculate acceleration is:
acceleration = force / mass
In this case, the initial mass of the loaded truck is M, and the final mass (after losing its load) is 0.1M. The initial acceleration is A.
So we have:
A = F / M
Now, we want to find the change in acceleration by comparing it to the initial acceleration for the same driving force. Let's call the change in acceleration ΔA.
The final acceleration (after losing its load) can be expressed as:
A - ΔA = F / (0.1M)
Rearranging this equation, we have:
ΔA = A - F / (0.1M)
To find the factor by which the acceleration must change, we can calculate the ratio of the change in acceleration to the initial acceleration:
factor = ΔA / A
Substituting the values we have so far, we get:
factor = (A - F / (0.1M)) / A
Let's plug in the given acceleration value: A = 4 m/s^2.
factor = (4 - F / (0.1M)) / 4
Unfortunately, we don't have the value for force (F) or mass (M), so we can't calculate the exact factor. However, if we knew the values for force and mass, we could substitute them into the equation to find the desired factor.