The roller-coaster car shown in fig. 6-41 (h1 = 45 m, h2 = 16 m, h3 = 26 m), is dragged up to point 1 where it is released from rest. assuming no friction, calculate the speed at points 2, 3, and 4.

There are many ways to solve this but I prefer to use the energy method. Calculate the potential energy using the point then from Potential Energy convert to Kinetic Energy at each points.

PE = KE

From the given points (h1 = 45, h2 = 16, h3  = 26)

Let’s use the formula: 

v2= sqrt[2*Gravity*h1]  where the gravity is equal to 9.81m/s2

v3= sqrt[2*Gravity*(h1 - h3 )] where the gravity is equal to 9.81m/s2

v4= sqrt[2*Gravity*(h1 – h2)] where the gravity is equal to 9.81m/s2

Solve for v2

v2= sqrt[2*Gravity*h1]      

    = √2*9.81m/s2*45m

v2= 29.71m/s

v3= sqrt[2*Gravity*(h1 - h3 )   

    =√2*9.81m/s2*(45-26)

    =√2*9.81m/s2*19 

v3=19.31m/s

v4= sqrt[2*Gravity*(h1 – h2)]        

    =√2*9.81m/s2*(45-16)

    =√2*9.81m/s2*(29)

v4=23.85m/s

b. latent learning (the word "latent" itself means something that exists but isn't obvious, only under certain conditions! )

the small 0.38-kg slider is known to move from position a to position b along the vertical-plane slot. determine (a) the work done on the body by its weight and (b) the work done on the body by the spring. the distance r = 0.70 m, the spring modulus k = 154 n/m, and the unstretched length of the spring is 0.53 m

explanation:

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