A 1.00-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P8.62a). The object has a speed of vi = 3.00 m/s when it makes contact with a light spring (Fig. P8.62b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Fig. P8.62c). The object is then forced toward the left by the spring (Fig. P8.62d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Fig. P8.62e). Find (a) the distance of compression d, (b) the speed vat the unstretched posi-tion when the object is moving to the left (Fig. P8.624), and (c) the distance D where the abject comes to rest.
Figure P8.62
(a)
The distance of the compression.
Answer to Problem 8.62AP
The distance of the compression is
Explanation of Solution
Given info: The mass of the object is
The formula to calculate the change in energy is,
Here,
The formula to calculate the initial kinetic energy of the object is,
Here,
The formula to calculate the final kinetic energy is,
Here,
The formula to calculate initial potential energy is,
Here,
Thus the initial potential energy of the block is
The formula to calculate the final potential energy is,
Here,
Thus, the final potential energy of the block is
The formula to calculate the initial energy is,
Here,
Substitute
Thus, the initial energy is
The formula to calculate the final energy is,
Here,
Substitute
Thus, the final energy is
The formula to calculate the law of conservation of energy between the second and third diagram is,
Here,
Substitute
Substitute
Substitute
Further solve the above equation.
Conclusion:
Therefore, the distance of the compression is
(b)
The speed at the unstretched position when the object is moving to the left.
Answer to Problem 8.62AP
The speed at the unstretched position when the object is moving to the left is
Explanation of Solution
Given info: The mass of the object is
The formula to calculate the change in energy is,
Here,
The formula to calculate the law of conservation of energy between the second and fourth diagram is,
Here,
Substitute
Substitute
Substitute
Conclusion:
Therefore, the speed at the unstretched position when the object is moving to the left is
(c)
The distance where the object comes to rest.
Answer to Problem 8.62AP
The distance where the object comes to rest is
Explanation of Solution
Given info: The mass of the object is
The formula to calculate the change in energy is,
Here,
Thus, the value of change in energy is
The formula to calculate the law of conservation of energy between the second and fifth diagram is,
Here,
Substitute
Substitute
Substitute
Conclusion:
Therefore, the distance where the object comes to rest is
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Chapter 8 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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