At rest Loading platform A 1000 kg roller coaster cart is initially at rest 100

Question

At rest Loading platform A 1000 kg roller coaster cart is initially at rest 100 meters above the passenger loading platform. The cart then rolls down the frictionless track to the bottom. Use the loading platform at the ground as the GPE reference (zero). What is the initial GPE, KE and total energy of the cart? What is the final GPE, KE, and total energy of the cart? (Hint: Use conservation of energy). If it takes 150 seconds for the roller coaster cart to get lifted from the ground to the highest point above the ground (100m) , what is the power of the motor that lifts the cart? SORT mass of cart, m = Y-Position at the highest point above the ground, Velocity at the highest point above the ground, m/s kg Yo - Voy

Explanation / Answer

m = mass = 1000 kg

u = initial velocity = 0 m/s( at rest)

h = height = 100 m

GPE _initial = mgh

= 1000*9.8*100 = 98*104 J

K.E_initial = (1/2)*m*u2 = 0

T.E _initial = GPE_initial + K.E_initial

= 98*104 + 0 = 98*104 J

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now h = 0

GPE_final = 1000*9.8*0 = 0 J

K.E_final = (1/2)*m*V2

V( final velocity) = ?

from V2 - u2 = 2*a*S

V2 - 0 = 2*g*h

V = ( 2*9.8*100)1/2 = 44.27 m/s

K.E_final = (1/2)*1000*(44.27)2 = 97.99*104 J

T.E_final = 0+ 97.99*104 J =  97.99*104 J

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t = time = 150 s

work done,W = change in K.E = K.E_final - K.E_initial

W =  97.99*104 J - 0 =  97.99*104 J

P(power) = W/t

P =  97.99*104 J / 150 s = 6532.67 watts

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