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
Want to see more full solutions like this?
Chapter 9 Solutions
Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
- 2. Consider the situation described in problem 1 where light emerges horizontally from ground level. Take k = 0.0020 m' and no = 1.0001 and find at which horizontal distance, x, the ray reaches a height of y = 1.5 m.arrow_forward2-3. Consider the situation of the reflection of a pulse at the interface of two string described in the previous problem. In addition to the net disturbances being equal at the junction, the slope of the net disturbances must also be equal at the junction at all times. Given that p1 = 4.0 g/m, H2 = 9.0 g/m and Aj = 0.50 cm find 2. A, (Answer: -0.10 cm) and 3. Ay. (Answer: 0.40 cm)please I need to show all work step by step problems 2 and 3arrow_forwardFrom number 2 and 3 I just want to show all problems step by step please do not short cut look for formulaarrow_forward
- Look at the answer and please show all work step by steparrow_forward3. As a woman, who's eyes are h = 1.5 m above the ground, looks down the road sees a tree with height H = 9.0 m. Below the tree is what appears to be a reflection of the tree. The observation of this apparent reflection gives the illusion of water on the roadway. This effect is commonly called a mirage. Use the results of questions 1 and 2 and the principle of ray reversibility to analyze the diagram below. Assume that light leaving the top of the tree bends toward the horizontal until it just grazes ground level. After that, the ray bends upward eventually reaching the woman's eyes. The woman interprets this incoming light as if it came from an image of the tree. Determine the size, H', of the image. (Answer 8.8 m) please show all work step by steparrow_forwardNo chatgpt pls will upvotearrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning