- #1
suffian
I am having trouble verifying my answer for a textbook Work-Energy-Power problem. The problem is stated below verbatim from the text. My difficulty appears to arise in part (c), though it might be coming earlier.
a) Okay, so let's denote the power output by the diesal units on the rest of the cars as P. Then this output should equal the forward force applied to the rest of the cars multiplied by their velocity, or P = Fv. Now, the forward force supplied will need to be n times the force it takes to keep one car steady at 27 m/s. So now the equation becomes P = nfv. If we isolate n then we can get a numerical answer:
n = \frac{P}{fv} = \frac{ \left[ 13.4 \times 10^6 \text{ W} \right] }{ \left[ 2800 \text{ N} \right] \left[ 27 \text{ m/s} \right] } \approx 177 \text{ (cars)}
b) Allright, when the train is accelerating then Newton's second law is in effect. The net force acting on the train happens to be the extra force needed to maintain the acceleration, f = ma. The mass of the train is the total mass of the diesal units plus the mass of all the car. Thus we have:
f = (m_d + n\, m_c)a = ( \left[1.10 \times 10^6 \text{ kg} \right] + [177][ 8.2 \times 10^4 \text{ kg} ] ) \left[ 0.10 \text{ m/s2} \right]
f = 1.56 \text{ MN}
When the train is going up a slope of angle \alpha, then it's own weight is pulling it down the incline by a force equal to mg \sin \alpha. If the train is to be in equilibrium, then it must negate this force by applying an additional force equal to this in the opposite direction (up the incline). Thus we have:
f = mg \sin \alpha = (m_d + n\, m_c)g \sin \alpha
f = ( \left[1.10 \times 10^6 \text{ kg} \right] + [177][ 8.2 \times 10^4 \text{ kg} ] ) [9.80 \text{ m/s2}] \sin\tan^{-1}(0.010))
f = 1.53 \text{ MN}
Close enough to each other.
c) Finally, here is where the problem arises. The book says that the extra power needed when traveling uphill at 1.0% slope is 2.9 MW, but I'm not getting that answer.
I figure that the extra power needed is the additional force that needs to be applied to the train to maintain equilibrium going uphill multiplied by the velocity. The additional force needed was found in part (b) and the velocity is 27 m/s. However, this would yield an extra power of 40 MW, a far cry from 2.9 MW. Can someone see what's going wrong?
a) Okay, so let's denote the power output by the diesal units on the rest of the cars as P. Then this output should equal the forward force applied to the rest of the cars multiplied by their velocity, or P = Fv. Now, the forward force supplied will need to be n times the force it takes to keep one car steady at 27 m/s. So now the equation becomes P = nfv. If we isolate n then we can get a numerical answer:
n = \frac{P}{fv} = \frac{ \left[ 13.4 \times 10^6 \text{ W} \right] }{ \left[ 2800 \text{ N} \right] \left[ 27 \text{ m/s} \right] } \approx 177 \text{ (cars)}
b) Allright, when the train is accelerating then Newton's second law is in effect. The net force acting on the train happens to be the extra force needed to maintain the acceleration, f = ma. The mass of the train is the total mass of the diesal units plus the mass of all the car. Thus we have:
f = (m_d + n\, m_c)a = ( \left[1.10 \times 10^6 \text{ kg} \right] + [177][ 8.2 \times 10^4 \text{ kg} ] ) \left[ 0.10 \text{ m/s2} \right]
f = 1.56 \text{ MN}
When the train is going up a slope of angle \alpha, then it's own weight is pulling it down the incline by a force equal to mg \sin \alpha. If the train is to be in equilibrium, then it must negate this force by applying an additional force equal to this in the opposite direction (up the incline). Thus we have:
f = mg \sin \alpha = (m_d + n\, m_c)g \sin \alpha
f = ( \left[1.10 \times 10^6 \text{ kg} \right] + [177][ 8.2 \times 10^4 \text{ kg} ] ) [9.80 \text{ m/s2}] \sin\tan^{-1}(0.010))
f = 1.53 \text{ MN}
Close enough to each other.
c) Finally, here is where the problem arises. The book says that the extra power needed when traveling uphill at 1.0% slope is 2.9 MW, but I'm not getting that answer.
I figure that the extra power needed is the additional force that needs to be applied to the train to maintain equilibrium going uphill multiplied by the velocity. The additional force needed was found in part (b) and the velocity is 27 m/s. However, this would yield an extra power of 40 MW, a far cry from 2.9 MW. Can someone see what's going wrong?
