Inclined PLane Force problem

[chimez14]

Homework Statement

Question:
An engine is used to pull a train of two cars out of a mine. The floor slopes upward at an angle of 22 degrees. Each car has a mass of 1.1x10^4 Kg and normally travels without friction on the tracks. The engine can exert a maximum force of 1.6x10^5 N on car A. If the engineer again throttles back so that the force exerted by the engine on car A decreases at the constant rate of 2.9 N per second, how long before the train stops moving up the track? Assume the original speed was 3.4 m/s

Homework Equations

F= Fmax-2.9t
acceleration=(Fmax-2.9t-mgsin(x))/m

The Attempt at a Solution

[(Fmax-mgsin(x))/m]T-[(1.45/m)]T^2=0
incase u havnt realized we're solving for "T"

 

[lippyka]

[(1.6x10^5-1.1x10^4 x 9.8 xsin22)/1.1x10^4]T-[(1.45/1.1x10^4)]T^2=0[1.48x10^5/1.1x10^4]T-[1.45/1.1x10^4]T^2=01.34T-1.45T^2=0T^2-1.34T+1.45=0(T-1.09)(T-1.32)=0T=1.09 or T=1.32The train will stop moving up the track in 1.09 seconds or 1.32 seconds.

 

[Moetasim]

I would approach this problem by first breaking down the given information and identifying the key variables and equations involved. From the statement, we can see that the problem involves a force (F), mass (m), acceleration (a), and time (t). Additionally, we are given the maximum force the engine can exert (Fmax) and the angle of inclination (x). Using the given equations, I would first find the acceleration of the train by plugging in the values for Fmax, m, and x. This will give me the acceleration in terms of t, which I can then use to solve for t by setting the equation equal to zero. This will give me the time it takes for the train to stop moving up the track.

Next, I would consider the implications of the engine throttling back at a constant rate of 2.9 N per second. This means that the force exerted by the engine on car A will decrease over time, leading to a decrease in acceleration. Therefore, I would need to modify the original equation to take into account this decrease in force. I would then use this new equation to solve for t once again.

Finally, I would compare the two values for t and determine the difference between them. This would give me the amount of time it takes for the train to stop moving up the track after the engine throttles back.

In conclusion, as a scientist, I would analyze the given information, use relevant equations to solve for the unknown variable, and consider any changes or modifications that may affect the final solution.