Mechanics - work done conservation of energy *Help needed*

[EddyH]

Homework Statement

A train with a mass of 250 tonnes starts from rest and accelerates up an incline of 1 in 100 attaining a speed of 45 Kph after traveling 200m. If the frictional resistance to motion is constant at 30KN calculate the work done by the engine using the principle of conservation of energy

Homework Equations

Possible relevant equations:

Work done= Force*Distance
Force=Mass*acceleration
Kinetic energy = 1/2*Mass*Velocity^2
Potential energy= Mass*Gravity (9.81)* Height

The Attempt at a Solution

Force= 250*103 Kg*12.5= 3 125 000 kg/m/s
Work done= 3 125 000*200= 625 000 000(J)
Not sure whether this is along the right lines or not. I am also unsure where the frictional resistance and gravity is used.

Thank you for your time.

 

[PhanthomJay]

Homework Statement

A train with a mass of 250 tonnes starts from rest and accelerates up an incline of 1 in 100 attaining a speed of 45 Kph after traveling 200m. If the frictional resistance to motion is constant at 30KN calculate the work done by the engine using the principle of conservation of energy

Homework Equations

Possible relevant equations:

Work done= Force*Distance
Force=Mass*acceleration
Kinetic energy = 1/2*Mass*Velocity^2
Potential energy= Mass*Gravity (9.81)* Height

The Attempt at a Solution

Force= 250*103 Kg*12.5= 3 125 000 kg/m/s

net force is mass times acceleration. You are not using the net force or the acceleration.

Work done= 3 125 000*200= 625 000 000(J)

Your incorrect values are calculating the net total work done. You are looking for the work done by the engine only.

Not sure whether this is along the right lines or not. I am also unsure where the frictional resistance and gravity is used.

Thank you for your time.

the problem is asking you to use conservation of energy, not force and kinematic equations. What is the conservation of energy equation that relates work and energy?

 

[EddyH]

Sorry to be a pain, but I do not know how to go about this, please can you explain?
Thank you

 

[PhanthomJay]

Say, Eddy, if you are asked to solve the problem using energy methods, you should know about the possible energy equations to use, for example, you should know that the work done by non conservative forces (like the engine force and friction force in this example) must equal the change in PE plus the change in KE of the system. Give it a try.

 

[asteriatic]

Hello,

Thank you for reaching out for help. The attempt at a solution is on the right track, but there are a few areas that need clarification and correction.

First, let's define the terms and concepts that are relevant to this problem. Work is defined as the product of a force and the distance over which that force acts. In this case, the force we are interested in is the force generated by the train's engine to move the train up the incline. This force is equal to the product of the train's mass and its acceleration, as stated in the equation "Force = Mass * Acceleration." Keep in mind that the mass of the train is given in tonnes, so it will need to be converted to kilograms before using it in calculations.

Next, we need to consider the principle of conservation of energy. This principle states that energy cannot be created or destroyed, only transferred from one form to another. In this case, the train's engine is converting chemical energy into kinetic energy to move the train up the incline. This means that the work done by the engine must be equal to the change in the train's kinetic energy. In other words, the work done by the engine is equal to the difference between the train's final kinetic energy and its initial kinetic energy.

Now, let's address the issue of frictional resistance and gravity. Frictional resistance is a force that opposes motion and is caused by the interaction between two surfaces. In this case, the frictional resistance is acting in the opposite direction of the train's motion, so it will need to be subtracted from the force generated by the engine. Gravity, on the other hand, is a force that acts downwards and is responsible for the train's potential energy. As the train moves up the incline, it gains potential energy, which can be calculated using the equation "Potential Energy = Mass * Gravity * Height."

Putting all of this together, the work done by the engine can be calculated using the following steps:

1. Convert the train's mass from tonnes to kilograms: 250 tonnes = 250,000 kilograms

2. Calculate the force generated by the engine using the equation "Force = Mass * Acceleration." In this case, the acceleration can be calculated using the incline's slope and the train's final speed. Remember to take into account the direction of the force and the frictional resistance.

3. Calculate the train's initial and final kinetic energies using the equation "Kin