
Concept explainers
(a)
To show force exerted by the springs on the particle is
(a)

Answer to Problem 68P
The force exerted by the springs on the particle is shown as
Explanation of Solution
Figure 1 represents two springs attached to mass
Write the expression for force.
Here,
From Figure 1 the new length is given as
Apply the above condition in equation (I).
From Figure 1, the angle cosine of
Use equation (III) in (II).
Conclusion:
Therefore, the force exerted by the springs on the particle is shown as
(b)
To show potential energy of the system is
(b)

Answer to Problem 68P
The potential energy of the system is shown as
Explanation of Solution
From subpart (a) force is
Write the potential energy of the system.
Here,
Use equation (IV) in (V) and Integrate Equation (V) from
Conclusion:
Therefore, the potential energy of the system is shown as
(c)
To make a plot between
(c)

Answer to Problem 68P
The plot between
Explanation of Solution
Figure 1 represents the plot between
Conclusion:
Therefore, The plot between
(d)
The speed of the mass
(d)

Answer to Problem 68P
The speed of the mass
Explanation of Solution
From subpart (b) gravitational potential energy is given as
The speed of the particle is equal to the change in gravitational potential energy.
Rearrange equation (VI), to find
Conclusion:
Substitute
Substitute
Therefore, the speed of the mass
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Chapter 6 Solutions
Principles of Physics: A Calculus-Based Text
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