(a)
The gravitational potential energy of block-Earth system.
(a)
Explanation of Solution
Given:
The mass of two blocks are
The length of mass
Formula used:
The energy contained in an object due to its position when compared to other objects is called potential energy. The two object system’s potential energy is the sum of energies of individual object.
Consider the horizontal line as datum line; it means
Write the expression for potential energy of block1.
Here,
Write the expression for potential energy of block2.
Here,
Write the expression for potential energy of two blocks system.
Here,
Calculation:
Calculate the height for block1.
Substitute
Calculate the height for block2.
Substitute
Substitute
Conclusion:
Thus, the gravitational potential energy of block-Earth system is
(b)
The angle where potential energy is minimum.
(b)
Explanation of Solution
Given:
The mass of two blocks are
The length of mass
Formula used:
The energy contained in an object due to its position when compared to other objects is called potential energy. The two object system’s potential energy is the sum of energies of individual object.
Consider the horizontal line as datum line; it means
Write the expression for potential energy of block1.
Here,
Write the expression for potential energy of block2.
Here,
Write the expression for potential energy of two blocks system.
Here,
The equilibrium points lies where first derivative of energy is zero. The potential energy would minimum on those points where the second derivative of energy is greater than zero.
Calculation:
Calculate the height for block1.
Substitute
Calculate the height for block2.
Substitute
Substitute
Calculate the equilibrium points.
The angle for equilibrium position is
Calculate the second derivative of potential energy.
Consider the value
For
For
Conclusion:
Thus, the angle where potential energy is minimum is
(c)
The gravitational potential energy of block-Earth system when
(c)
Explanation of Solution
Given:
The mass of two blocks are
The length of mass
Formula used:
The energy contained in an object due to its position when compared to other objects is called potential energy. The two object system’s potential energy is the sum of energies of individual object.
Consider the horizontal line as datum line; it means
Write the expression for potential energy of block1.
Here,
Write the expression for potential energy of block2.
Here,
Write the expression for potential energy of two blocks system.
Here,
Calculation:
Calculate the height for block1.
Substitute
Calculate the height for block2.
Substitute
Substitute
For
Conclusion:
Thus, the gravitational potential energy of block-Earth system is zero always for
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Chapter 7 Solutions
Physics for Scientists and Engineers
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