Concept explainers
A small 0.65-kg box is launched from rest by a horizontal spring as shown in Figure P9.50. The block slides on a track down a hill and comes to rest at a distance d from the base of the hill. Kinetic friction between the box and the track is negligible on the hill, but the coefficient of kinetic friction between the box and the horizontal parts of track is 0.35. The spring has a spring constant of 34.5 N/m, and is compressed 30.0 cm with the box attached. The block remains on the track at all times.
a. What would you include in the system? Explain your choice.
b. Calculate d.
(a)
The items included in the system and explain the choice.
Answer to Problem 50PQ
The items included are the box and the tracks surface because the kinetic friction increases the thermal energies and included this thermal energy internal to the system.
Explanation of Solution
In order to keep all the thermal energy into the system, it is better to include both the box and the tracks surface so that it will increase the kinetic friction which leads to the increase in the thermal energies and including both keeps all of this thermal energy internal to the system.
If Earth and spring are the choices, to account for them in terms of changes in gravitational and elastic potential energy without letting anything outside the system to do work.
Figure 1 show the graph of the initial and final energies which will help to organize the energies needed to be taken into account.
Conclusion:
Therefore, the items included are box and the tracks surface because the kinetic friction increases the thermal energies and included this thermal energy internal to the system.
(b)
The value of
Answer to Problem 50PQ
The value of
Explanation of Solution
The reference configuration for the spring is when it is relaxed, and for gravity it is when the box is at the bottom of the ramp. The box is initially at rest
The energy conservation equation for a system is,
Here,
In this problem, Equation (I) will changes to (since all other energies are zero),
Write the expression for the initial gravitational potential energy.
Here,
Write the expression for the initial potential energy of the spring.
Here,
Write the expression for the thermal energy.
Here,
The total path length will be
Kinetic friction is proportional to the normal force which equals the weight.
Here,
Write the expression for the normal force.
Use equation (VIII) in equation (VI),
Use equation (VIII) in (VI), and solve for
Conclusion:
The displacement
Substitute
Therefore, the value of
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Chapter 9 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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