A 45-t electric train accelerates uniformly from a station with the train’s motion depicted in the graph in Figure 2.(Recall that 1 t = 1.0 × 103 kg.)Determine the net force acting on the train during the uniform acceleration portion of the motion.
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To determine the net force acting on the train during the uniform acceleration portion of the motion, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, we need to calculate the acceleration of the train. The graph in Figure 2 shows the velocity of the train changing linearly with time during the uniform acceleration portion. We can determine the acceleration by finding the slope of the velocity-time graph.
From the graph, we can see that the train's velocity changes from 0 m/s to 30 m/s over a time interval of 20 seconds. Using the formula for average acceleration:
acceleration = (change in velocity) / (time interval)
acceleration = (30 m/s - 0 m/s) / (20 s)
acceleration = 30 m/s / 20 s
acceleration = 1.5 m/s^2
Now that we have the acceleration, we can calculate the net force acting on the train. The mass of the train is given as 45 tons, which can be converted to kilograms:
mass = 45 tons * (1.0 × 10^3 kg/1 ton)
mass = 45 × 10^3 kg
Using Newton's second law:
net force = mass * acceleration
net force = (45 × 10^3 kg) * (1.5 m/s^2)
net force = 67.5 × 10^3 N
Therefore, the net force acting on the train during the uniform acceleration portion of the motion is 67.5 × 10^3 Newtons.