An empty truck weight4000N. Its engine can produce a maximum acceleration of 1m/s2. Ifthe truck is loaded with 2000N, find the maximum acceleration the engine can produce
the force is constant ... the acceleration is inversely proportional to the mass
a = [4000 / (4000 + 2000)] * 1 m/s^2
To find the maximum acceleration the engine can produce when the truck is loaded with 2000N, we need to calculate the net force acting on the truck.
1. Start by calculating the net force when the truck is empty:
Net Force = Weight of the truck
= 4000N
2. Now, let's calculate the net force when the truck is loaded:
Net Force = Weight of the truck + Weight of the load
= 4000N + 2000N
= 6000N
3. The maximum acceleration the engine can produce is equal to the net force divided by the total mass of the truck:
Maximum Acceleration = Net Force / Total Mass
Since we know the net force (6000N) and need to find the maximum acceleration, we need to determine the total mass of the truck.
Let's assume the mass of the truck when empty is m1 and the mass of the load is m2.
Given:
Weight = Mass × Acceleration due to gravity
4000N = m1 × 9.8m/s^2
Solving for m1:
m1 = 4000N / 9.8m/s^2
m1 ≈ 408.16 kg
Similarly, for the loaded truck:
2000N = m2 × 9.8m/s^2
m2 = 2000N / 9.8m/s^2
m2 ≈ 204.08 kg
Now, the total mass of the truck is:
Total Mass = m1 + m2
= 408.16 kg + 204.08 kg
≈ 612.24 kg
Finally, we can find the maximum acceleration using the net force and total mass:
Maximum Acceleration = 6000N / 612.24 kg
Maximum Acceleration ≈ 9.8 m/s^2
Therefore, the maximum acceleration the engine can produce when the truck is loaded with 2000N is approximately 9.8 m/s^2.