Answer:
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Answer : x ( acceleration of mass 4m ) =
The top pulley rotates because it has to keep the center of mass of the system at equilibrium
Explanation:
Given data:
mass suspended = 4 meters
mass suspended at other end = 3 meters
first we have to express the kinetic and potential energy equations
The general kinetic energy of the system can be written as
T =
T =
also the general potential energy can be expressed as
U =
The Lagrangian of the problem can now be setup as
next we will take the Euler-Lagrange equation for the generalized equations :
Euler-Lagrange equation =
solving the equations simultaneously
x ( acceleration of mass 4m ) =
The top pulley rotates because it has to keep the center of mass of the system at equilibrium
Answer:
ω = 4.07 rad/s
Explanation:
By conservation of the energy:
W = ΔK
where
Solving for ω:
The horizontal distance traveled below the table's edge is 29.4 cm.
The given parameters;
- <em>mass of the bullet, = 15 g = 0.015 kg</em>
- <em>speed of the bullet, = 630 m/s</em>
- <em>mass of the block, = 4.9 kg</em>
The final velocity of the bullet-block system is calculated as follows;
The time for the bullet-block system to reach the ground from the table is calculated as follows;
The horizontal distance traveled below the table's edge is calculated as follows;
Thus, the horizontal distance traveled below the table's edge is 29.4 cm.
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