How Do You Calculate the Velocity of a Mine Car Hoisted Up an Incline?

  • Thread starter joemama69
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In summary, a 400kg mine car is being hoisted up an incline using a cable and motor. The force in the cable can be represented by F=3200t^2 N, where t is in seconds. With an initial velocity of v=2 m/s @ t=0, the car's velocity @ t=2 can be determined by summing the forces in the x direction, which is parallel to the slope of the hill. This results in an acceleration of a=8t^2 - 4.616. Integrating this to find the velocity, we get v=8/3 t^3 - 4.616t+c, with c=2. Plugging in t=2,
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joemama69
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Homework Statement


A 400kg mine car is hoisted up the incline (8,15,17 Triangle which i calculated the angle to be 28.0724 degrees)using a cable and motor. For a short time, the force in the cable is F=3200t^2 N, where t is in seconds. If the car has an initial velocity v=2 m/s @ t=0, determine its velocity @ t=2.


Homework Equations



F=ma

The Attempt at a Solution



Since there is no friction i believe that the Y forces don't matter nore does the Normal.
So I sumed the forces in the x direction which is parallel to the slope of the hill.

E F(x)=F-mgsin(theta)=ma i got a=8t^2 - 4.616...

i then integrated a to get v=8/3 t^3 - 4.616t+c c= 2. pluged in t=2 and got v=14.10 m/s


is this correct
 
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looks correct...
 
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?

Yes, your solution is correct. By summing the forces in the x-direction, you have correctly accounted for the acceleration of the mine car. Your integration and substitution are also correct, resulting in a final velocity of 14.10 m/s at t=2 seconds. Great job!
 

FAQ: How Do You Calculate the Velocity of a Mine Car Hoisted Up an Incline?

What is motion rectilinear coord?

Motion rectilinear coord is the study of an object's motion in a straight line, using a coordinate system to describe its position, velocity, and acceleration.

What are the basic components of motion rectilinear coord?

The basic components of motion rectilinear coord are position, velocity, and acceleration. Position refers to the location of the object in the coordinate system, velocity is the rate of change of position over time, and acceleration is the rate of change of velocity over time.

How do you calculate an object's position in motion rectilinear coord?

An object's position in motion rectilinear coord can be calculated using the formula x = x0 + v0t + 1/2at2, where x is the final position, x0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time elapsed.

What is the difference between speed and velocity in motion rectilinear coord?

Speed refers to the rate of motion of an object, while velocity is the rate of motion in a specific direction. In motion rectilinear coord, velocity takes into account the direction of motion, while speed does not.

What is the relationship between velocity and acceleration in motion rectilinear coord?

Velocity is the rate of change of an object's position, while acceleration is the rate of change of an object's velocity. This means that acceleration is the second derivative of an object's position, and is therefore related to velocity in motion rectilinear coord.

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