If a loaded truck that can accelerate at 1 m/s2 loses its load and has four-fifths of its original mass, what acceleration can it attain if the same driving force acts on it?
acceleration = net force/mass
acceleration = 1/.8(4/5)
acceleration = 1.25 m/s^2
hope this helps!!!!
Well, losing a load can be quite enlightening for a truck, don't you think? It's like shedding some pounds and feeling lighter on your wheels! So, with four-fifths of its original mass, this truck can potentially accelerate at the same rate as before, because it's carrying less...let's say...cargo. So, it can still manage a dazzling acceleration of 1 m/s²! Just don't tell the truck; it might feel a bit insecure about losing weight so easily!
To solve this problem, let's break it down step-by-step:
Step 1: Determine the original mass of the loaded truck.
Let's assume that the original mass of the loaded truck is M.
Step 2: Calculate the mass of the truck after losing its load.
The problem states that the truck has four-fifths of its original mass, which means its mass is now (4/5) * M.
Step 3: Calculate the acceleration of the truck with the original driving force.
The driving force acting on the truck remains the same. Therefore, we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a). In this case, F remains constant, and we need to solve for the new acceleration (a').
F = m * a
F = M * a
Step 4: Substitute the new mass into the equation.
F = (4/5) * M * a'
Step 5: Rearrange the equation to solve for the new acceleration.
To determine the new acceleration (a'), we can rearrange the equation:
a' = (F * 5) / (4 * M)
Step 6: Simplify the equation.
a' = (5F) / (4M)
Therefore, the acceleration the truck can attain after losing its load is (5F) / (4M).
To find the new acceleration of the truck, we need to use the principle of conservation of momentum. The principle states that the total momentum of a system remains constant if no external forces act on it.
Let's break down the problem step by step:
Step 1: Determine the original acceleration of the loaded truck.
Given that the loaded truck can accelerate at 1 m/s², we can identify the original acceleration as "a = 1 m/s²."
Step 2: Determine the original mass of the loaded truck.
Since the truck loses four-fifths of its original mass, its new mass is one-fifth (1 - 4/5 = 1/5) of the original mass. Let's denote the original mass as "m," and the new mass as "m'." Therefore, we have "m' = 1/5m."
Step 3: Apply the principle of conservation of momentum.
According to the principle of conservation of momentum, the momentum before the load is lost and after the load is lost should be the same.
Momentum (p) is given by the product of mass (m) and velocity (v): p = mv.
Before the load is lost, the momentum is given by m * v, and after the load is lost, the momentum is given by m' * v', where v and v' are the velocities before and after the load is lost, respectively.
Since the driving force acting on the truck remains the same, we can assume the velocities before and after the load is lost are the same. Therefore, v = v', and the equation becomes m * v = m' * v'.
Step 4: Solve for the new acceleration.
Using the expression for mass that we found in step 2 (m' = 1/5m), we can substitute it into the conservation of momentum equation: m * v = (1/5m) * v.
Cancel out the "m" terms: v = (1/5) * v.
This equation shows that the velocities before and after the load is lost are the same.
Since acceleration (a) is the derivative of velocity with respect to time (a = dv/dt), and the velocity remains the same, the new acceleration is also 1 m/s².
Therefore, the truck can attain the same acceleration of 1 m/s² even after losing the load.