A loaded truck can accelerate at 4.1 m/s
2
. It
loses its load so that it is only 0.8 as massive.
By what factor must the acceleration
change for the same driving force?
F = M1 A1 = M2 A2
M2 = .8 M1
M1 A1 = .8 M1 A2
A2 = (1/.8) A1
A2 = 1.25 A1
To find the factor by which the acceleration must change, we need to compare the initial situation (loaded truck) with the final situation (truck after losing the load).
Let's assume the initial acceleration of the loaded truck is a1 (4.1 m/s^2). We can represent the mass of the loaded truck as m1.
The mass of the truck after losing the load is given as 0.8 times the mass of the loaded truck (m1). Therefore, the mass of the truck after losing the load is 0.8 * m1.
Now, let's find the acceleration of the truck after losing the load. Let's assume it is a2.
According to Newton's second law of motion, the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a). Therefore, the force acting on the loaded truck is m1 * a1, and the force acting on the truck after losing the load is (0.8 * m1) * a2.
Since both situations involve the same driving force, we can set the two forces equal to each other:
m1 * a1 = (0.8 * m1) * a2
Now, we can cancel out m1 from both sides of the equation:
a1 = 0.8 * a2
To find the factor by which the acceleration must change, we can divide both sides of the equation by a1:
1 = 0.8 * (a2 / a1)
Simplifying further:
(a2 / a1) = 1 / 0.8
(a2 / a1) = 1.25
Therefore, the factor by which the acceleration must change for the same driving force is 1.25.