5. Two blocks slide without friction on separate tracks that start 1.00 m above

Question

5. Two blocks slide without friction on separate tracks that start 1.00 m above the ground. The first track is sloped down at a steady 15.0°; the second drops almost straight down, and then winds along the ground with a total path length of 4.5 m. The two tracks end in the same place. a. Which block gets there first? Show your work in detail. b. What if we add friction to the second path? Is it possible for the winner to change? What is the minimum coefficient of friction necessary to change the winner? Assume friction only is significant once the block is at ground level. Answers: (a) Second block wins (b) yes, ,-0.27 ]

Explanation / Answer

the initial velocity of both blocks= 0 m/s

First block ,a = g sins theta= 9.8 sin(15) =2.536 m/s^2

dispalcemnet for first block = 1m/ sin 15 = 3.864 m apprx

s= 1/2 at^2

time to reach the bottom by first block = sqroot (2 x 3.864 / 2.536) =1.745 seconds apprx

second block,

a= 9.8 m/s^2

time to cover vertical height = sqroot ( 2/9.8) =0.4157 seconds

velocity at bottom for second block =

mgh = 1/2 mv^2

v = sqroot ( 2gh) = 4.427 m/ s apprx

time to travel on ground= ( 4.5-1)/ 4.427 = 0.7906 seconds

total time for second block =0.4157 + 0.7906=1.206 seconds apprx

second stone will reach faster,

b)yes, friction will reduce velocity and increase time

c) a ( retardation ) = mu (9.8)

time should be= (1.745 - 0.4157 )= 1.329 seconds apprx

3.5 = 4.427 (1.329) - 0.5 (mu (9.8)) (1.329))^2

2.383/8.654 = (mu)

mu =0.27 apprx

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