A train slows from 25m/s to 14m/s in 5.0s. Calculate the work done on the train....so I calculted the displacement and the force and put them together to get an answer of 5.0 x 10^7J, but my textbook says it should be 1.1 x 10^7J? Am I right, or is the textbook?
Merci beaucoup!
I don't know how you can do this without the mass of the train.
work done= change in KE
= 1/2 mass (25^2 -14^2)
i have the textbook, mass is 52 000kg
d = (v1 + v2)1/2 x t
a = change in velo/time
f = m x a
plug in numbers to w = fd
To determine whether your answer or the textbook's answer is correct, let's go through the steps to calculate the work done on the train.
The work done on an object is given by the equation:
Work = Force x Displacement x cos(theta)
In this case, the train is slowing down, so the force exerted on it is in the opposite direction of its motion. Therefore, the angle between the force and the displacement is 180 degrees, and cos(theta) would be -1.
First, let's find the force exerted on the train using Newton's second law:
Force = mass x acceleration
To find the mass of the train, we need to know the net force acting on the train. Given that the train is slowing down, we can assume that the net force is due to friction. Therefore, the net force is the force of friction:
Force = friction
The force of friction can be calculated using the equation:
friction = coefficient of friction * normal force
The normal force is equal to the weight of the train, which can be calculated using:
weight = mass x gravity
In this case, we don't know the coefficient of friction or the mass of the train, so we can't calculate the force of friction directly. However, we can use the given information to find the force.
The information given is the initial and final velocities of the train and the time it takes to change the velocity. To find the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Once we have the acceleration, we can use Newton's second law to find the force, which is equal to mass times acceleration.
Next, we need to calculate the displacement of the train. Since the train is slowing down, the displacement is the distance traveled during the time interval. The formula to calculate displacement is:
displacement = ((initial velocity + final velocity) / 2) x time
Finally, we can calculate the work done on the train using the equation:
Work = Force x Displacement x cos(theta)
Substitute the values you have calculated into the equation and check if you get the same answer as the textbook's 1.1 x 10^7J.
If there are any discrepancies between your calculations and the textbook's answer, double-check your calculations and ensure that you have used the correct formulas and correctly substituted the values.