How far did the train travel before stopping after detaching a compartment?

AI Thread Summary
The discussion revolves around calculating the distance a train travels after its last compartment detaches while moving up a 4-degree incline at 5 m/s. Initial calculations yielded an incorrect distance of 0.09 m, prompting a request for clarification. A more accurate approach involves equating the initial kinetic energy of the compartment to its potential energy at the maximum height reached. By applying trigonometry to convert the height into distance along the incline, a correct distance of over 18 m is determined. The conversation emphasizes the importance of correctly interpreting the problem and applying energy conservation principles.
mrhobbes
Messages
3
Reaction score
0
A train moving up an incline at 4 degrees has it's last train compartment detached. The train was moving at a speed of 5 m/s when the compartment breaks free. How far did the train get before the speed momentarily reaches zero?

No other information is given, but using all that was provided, I got a ridiculously small answer of 0.09 m. I got this by splitting up my speed into x and y components and then using the Vo(y) in the equation d= vf² - vo² / 2a to get my vertical displacement. I then used distance to get my inclined displacement by using sin 5 = y / r.

I checked the answer and it turns out that it was wrong. Could anyone give me any hints on how to solve the problem?

Thanks
 
Physics news on Phys.org
Welcome to PF.
The question doesn't make much sense as written. Perhaps it means a train CAR breaks free from the back of the train. Without engine. How far does the CAR go up the hill?

It's initial speed is 5 m/s. Since it is going up the hill, its KE will soon be converted into PE. You could begin with
initial KE = final PE
.5*mv² = mgh
and quickly find the height reached from the initial position. You'll have to convert that into a (larger) distance along the ramp with a bit of trigonometry. I'm getting a little more than 18 m.
 
Thank you so much. You were right.
 
Most welcome! Good luck with the next one.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

How far does the train travel before the engine is ....
Replies
2
Views
2K
Solving Detached Train Cart Problem: Find Distance
Replies
8
Views
2K
Ball bounces several times on an inclined plane
Replies
8
Views
3K
Calculate the force to stop a train
Replies
2
Views
7K
Kinematics on a frictionless incline plane
Replies
3
Views
2K
What is the displacement of a 3.0 kg block sliding down an inclined plane?
Replies
12
Views
2K
Morin 3.7 -- Block sliding sideways on an inclined plane
Replies
11
Views
1K
Stopping Distance affected by Mass of Cart on Inclined Plane
Replies
1
Views
4K
Box and a Spring on on an inclined plane
Replies
11
Views
3K
How Far Does a Block Travel Up an Incline Before Stopping?
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top