(3 points) A disk is spinning freely with angular speed 6.0 rad/s when a second identical disk, initially not spinning, is dropp
ed on it so that their axes coincide. In a short time the two disks are co-rotating. a) Sketch the initial situation and the consequential situation. b) What is the angular speed of the new system? c) If a third such disk is dropped on the first two, find the final angular speed of the system.
1 answer:
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Answer:
Velocity is 2.17 m/s at an angle of 9.03° above X-axis.
Explanation:
Mass of object 1 , m₁ = 300 g = 0.3 kg
Mass of object 2 , m₂ = 400 g = 0.4 kg
Initial velocity of object 1 , v₁ = 5.00i-3.20j m/s
Initial velocity of object 2 , v₂ = 3.00j m/s
Mass of composite = 0.7 kg
We need to find final velocity of composite.
Here momentum is conserved.
Initial momentum = Final momentum
Initial momentum = 0.3 x (5.00i-3.20j) + 0.4 x 3.00j = 1.5 i + 0.24 j kgm/s
Final momentum = 0.7 x v = 0.7v kgm/s
Comparing
1.5 i + 0.24 j = 0.7v
v = 2.14 i + 0.34 j
Magnitude of velocity
Direction,
Velocity is 2.17 m/s at an angle of 9.03° above X-axis.
Answer:
a) Initial Value Problem
dv/dt = 4 - 0.1v
v(0) = 0
b) solution to the IVP
v(t) = 40(1 - e^(-t/10))
c) Limiting velocity
Vo = 40 ft/s
Position of the car after 12 hours
X = 14,390 ft
Explanations:
The complete explanations of each of the sections contained in the question are in the files attached to this solution.
