(a)
The final speed of bullet.
(a)
Answer to Problem 89AP
The final speed of bullet is
Explanation of Solution
In collision of the bullet with the block the momentum of the system remains conserved.
Write the expression for the conservation of momentum.
Here,
Write the expression for the initial momentum of the system.
Here,
Substitute
Write the expression for the final momentum of the system.
Here,
After the collision, the velocity acquired by block is used to compress the spring. Hence the kinetic energy is converted to potential energy.
Write the expression for conservation of energy.
Here,
Write the expression for the kinetic energy of the block.
Write the expression for the spring potential energy.
Here,
Substitute
Simplify the above expression for value of
Substitute
Substitute
Simplify the above equation for value of
Conclusion:
Substitute
Thus, the final speed of bullet is
(b)
The amount of initial kinetic energy of bullet converted to internal energy of bullet block system.
(b)
Answer to Problem 89AP
The amount of initial kinetic energy of bullet converted to internal energy of bullet block system is
Explanation of Solution
Difference in the final and initial kinetic energy gives the amount of internal energy.
Write the expression for the conservation of energy.
Here
Simplify the above equation for value of
Write the expression for the
Here
Write the expression for the final kinetic energy.
Write the expression for initial kinetic energy.
Substitute
Substitute
Conclusion:
Susbtitute
Thus, the amount of initial kinetic energy of bullet converted to internal energy of bullet block system is
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Chapter 9 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
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