A mass slider m = 0.200 kg rests on a frictionless horizontal air rail connected to a spring with a force constant k = 5.00 N /
m. You pull the slider, stretching the spring 0.100 m, and then release it from rest. The slider returns to its equilibrium position (x = 0). What speed does it have when x = 0.080 m?
1 answer:
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Answer: 288.8 m
Explanation:
We have the following data:
is the time it takes to the child to reach the bottom of the slope
is the initial velocity (the child started from rest)
is the angle of the slope
is the length of the slope
Now, the Force exerted on the sled along the ramp is:
(1)
Where is the mass of the sled and
its acceleration
In addition, if we draw a free body diagram of this sled, the force along the ramp will be:
(2)
Where is the acceleration due gravity
Then:
(3)
Finding :
(4)
(5)
(6)
Now, we will use the following kinematic equations to find :
(7)
(8)
Where is the final velocity
Finding from (7):
(9)
(10)
Substituting (10) in (8):
(11)
Finding :