Conservation of Mechanical Energy in truck

AI Thread Summary
The discussion centers on calculating the minimum length of a frictionless emergency escape ramp for a runaway truck moving at 150 km/h. The truck's mass is 5000 kg, and its kinetic energy at the bottom of the ramp is calculated to be 4,326,400 J. The potential energy at the top of the ramp is expressed as mgh, with the height determined using the ramp's inclination of 15°. Participants discuss the relationship between kinetic and potential energy to find the necessary height and subsequently the ramp length. The conversation concludes with a participant successfully grasping the concept and moving forward with the calculations.
kappcity06
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a runaway truck with failed brakes is moving downgrade at 150km/h (41.6 m/s) just before the driver steers the truck travel up a frictionless emergency escape ramp with an inclination of 15°. The truck's mass is 5000 kg.

What minimum length L must the ramp have if the truck is to stop (momentarily) along it? (Assume the truck is a particle).

i have its potenail enegry when it is at the top of the raqmp to be mgh or 49000sin15? I'm do not know if this is right. thekentic energy would be 1/2mv^2 or 4326400 at the bottom of the ramp. I am not sure where to go now. please help
 
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The potential energy at the top would be just mgh, or 49000h. You know the kinetic energy at the bottom. Now apply the title of your post to this data to find h. :smile:
 
ok i will try it
 
ok thanks i got it
 
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}...
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