General motion mechanics

In summary: The kinetic energy at speed 2V is Kv. The relationship between change in kinetic energy, power and time where the power is constant is K=Pv^2/2. Therefore, the time is 2*K and the corresponding distance is V*K.
  • #1
bernvall
19
0

Homework Statement


The resultant force acting on a train of mass m starting from rest on a level track is a constant P for speeds less than V . For speeds greater than V the power exerted by the resultant force has a constant value PV . Find the time taken to reach a speed 2V from rest, and the corresponding distance travelled.


Homework Equations



Force= power * velocity
Power= dw/dt

The Attempt at a Solution



for some reason, i don't know how to go about doing it.
 
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  • #2
bernvall said:

Homework Statement


The resultant force acting on a train of mass m starting from rest on a level track is a constant P for speeds less than V . For speeds greater than V the power exerted by the resultant force has a constant value PV . Find the time taken to reach a speed 2V from rest, and the corresponding distance travelled.


Homework Equations



Force= power * velocity
Power= dw/dt

The Attempt at a Solution



for some reason, i don't know how to go about doing it.
Since W = Fs, Power = dW/dt = Force * ds/dt = Force * velocity

What does the resultant force do to the train? (hint: Newton's 2nd law). That should allow you to determine time and distance in reaching V in terms of P and m (mass of the train). Does anything change when it hits speed V?

AM
 
  • #3
Yes, i realized that i needed to use Newtons 2nd Law.

What i did was split it up in two, from 0 to V and then from V to 2V. the first part i managed to find the time and distance easily using equations of motion. However for the second part i didn't know what the resultant force was. It gives you the power at 2V NOT the resultant, so i got stuck again.
 
  • #4
bernvall said:
Yes, i realized that i needed to use Newtons 2nd Law.

What i did was split it up in two, from 0 to V and then from V to 2V. the first part i managed to find the time and distance easily using equations of motion. However for the second part i didn't know what the resultant force was. It gives you the power at 2V NOT the resultant, so i got stuck again.
Let speed = v. Since Power = PV = Fv for v>V, then what is the force F?

What is the kinetic energy at speed 2V? What is the relationship between change in kinetic energy, power and time where the power is constant? That should give you the time. And from that you should be able to work out the distance.

AM
 
  • #5
I think we can use the equations of motion to solve this problem. First, we can set up the equation for force as F=ma, where m is the mass of the train and a is the acceleration. Since the train is starting from rest, we can also use the equation v=u+at, where v is the final velocity, u is the initial velocity (which is 0 in this case), and t is the time taken. We also know that the power exerted by the resultant force is constant (PV) for speeds greater than V.

From these equations, we can substitute the value of force (P) into the equation F=ma to get ma=P. We can then rearrange this to get a=P/m.

Next, we can use v=u+at to find the time taken (t) to reach a speed of 2V. Since u=0 and a=P/m, we get v=2V=0+P/m*t. Solving for t, we get t=2m/P.

To find the distance travelled, we can use the equation s=ut+1/2at^2. Since u=0, we get s=1/2 * P/m * (2m/P)^2=2m. Therefore, the time taken to reach a speed of 2V is 2m/P and the corresponding distance travelled is 2m.

In summary, the time taken to reach a speed of 2V from rest is 2m/P and the corresponding distance travelled is 2m. This shows that the time taken and the distance travelled are both dependent on the mass of the train and the constant power exerted by the resultant force. As the mass of the train increases, the time taken and the distance travelled will also increase. Similarly, if the constant power (PV) increases, the time taken and the distance travelled will decrease. This information can be useful in designing and optimizing train systems for efficient and safe travel.
 

1. What is general motion mechanics?

General motion mechanics is a branch of physics that studies the motion of objects in space and how they interact with their environment. It combines principles from both classical mechanics and special relativity to explain the behavior of objects in motion.

2. What are the three laws of motion?

The three laws of motion, also known as Newton's laws, are the fundamental principles of general motion mechanics. They state that an object will remain at rest or in uniform motion unless acted upon by a force, the force applied to an object is equal to its mass multiplied by its acceleration, and for every action, there is an equal and opposite reaction.

3. How does general motion mechanics apply to real-world situations?

General motion mechanics can be applied to a wide range of real-world situations, such as the motion of vehicles on a road, the movement of planets in our solar system, and the flight of airplanes. It helps us understand and predict the behavior of objects in motion, which is crucial in fields like engineering and astronomy.

4. What is the difference between linear and rotational motion?

Linear motion is when an object moves in a straight line, while rotational motion is when an object rotates around a fixed axis. Both types of motion follow the same principles of general motion mechanics, but they have different equations and behaviors.

5. How does general motion mechanics relate to energy and work?

General motion mechanics is closely related to the concepts of energy and work. The work done on an object is equal to the force applied multiplied by the distance it moves, and this work can change an object's kinetic energy. Additionally, the conservation of energy principle is a fundamental concept in general motion mechanics, stating that energy cannot be created or destroyed, only transferred or converted between different forms.

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