A loaded truck can accelerate at 3.2 m/s^2
It loses its load so that it is only 0.2 as massive. By what factor must the acceleration change for the same driving force?
since F=MA, and the mass is going to be 1/5 the amount it originally was, the acceleration must increase by a factor of 5.
Wow i definitely over thought that one. thank you so much for helping me! it means so much to me!
To solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
where F is the force, m is the mass, and a is the acceleration.
Let's assume the initial mass of the loaded truck is m1 and the final mass, after losing its load, is m2. According to the problem statement, m2 = 0.2 * m1.
Now, let's consider the force acting on the truck. Since the driving force remains the same, we can express the force as:
F = m1 * a1
where a1 is the initial acceleration of the loaded truck.
Considering the same driving force but with the reduced mass, the force acting on the truck after losing the load can be expressed as:
F = m2 * a2
where a2 is the final acceleration of the truck after losing the load.
However, we also know that m2 = 0.2 * m1, so we can substitute this into the equation:
F = (0.2 * m1) * a2
Since the driving force remains the same, we can set these two expressions for force equal to each other:
m1 * a1 = (0.2 * m1) * a2
Now, let's solve for a2:
a2 = (m1 * a1) / (0.2 * m1)
Simplifying the expression:
a2 = 5 * a1
Therefore, the acceleration must change by a factor of 5 for the same driving force.
To find the factor by which the acceleration must change, we need to consider the relationship between force, mass, and acceleration, which is given by Newton's second law of motion: Force = mass × acceleration.
Let's assume the original mass of the loaded truck is M, and its acceleration is A. Therefore, the force (F1) acting on the truck is given by F1 = M × A.
After losing its load, the mass of the truck becomes 0.2M. Now, we need to determine the new acceleration, let's call it A2, for the same driving force.
According to Newton's second law of motion, the force (F2) acting on the truck after losing its load is given by F2 = (0.2M) × A2.
Since the driving force remains the same, F1 = F2. So we can equate the two expressions for force:
M × A = (0.2M) × A2
Now, let's simplify the equation by canceling out the mass factor:
A = 0.2A2
Dividing both sides of the equation by 0.2A gives:
1 = A2/5
Therefore, the new acceleration (A2) must be five times the original acceleration (A) for the same driving force.