Concept explainers
A crate is given an initial speed of 3.0 m/s up the 25.0° plane shown in Fig. 4-60. (a) How far up the plane will it go? (b) How much time elapses before it returns to its starting point? Assume
Part(a)
The distance the block would go up an inclined plane when given an initial velocity.
Answer to Problem 58P
Solution:
The distance the block goes up the block is 0.29 m.
Explanation of Solution
Given:
The initial speed of the block
The angle of the incline
The speed of the block at the distance s is
Formula used:
A block is given an initial speed. Itslides up a distance s along the length of the incline which is at an angle
The free body diagram for the block is shown in the diagram below.
The weight mg of the crate acts vertically downwards. The normal force
Since there is no motion perpendicular to the incline,
The force of kinetic friction is related to the normal force as,
Since the crate slides up the incline, there is a net force F that acts downwards. This is given by,
Substitute equations (1) and (2) in (3).
From Newton’s second law,
Here, a is the resultant acceleration of the crate down the incline.
Therefore,
The distance s it travels up the slope is calculated using the equation,
Calculation:
Calculate the acceleration of the crate by substituting 9.8 m/s2for g and the given values for
Since the acceleration acts opposite to the direction of motion of the crate, a negative sign is affixed to the acceleration.
Calculate the distance the crate travels up the incline using the expression
Conclusion:
The motion of a block sliding up the inclined plane is analyzed by constructing its free body diagram. The acceleration of the block is determined using the free body diagram and Newton’s second law. Using the equations of motion, the distance the block slides up the plane is found to be 0.29m.
Part(b)
The time taken by the block t returns to the starting point.
Answer to Problem 58P
Solution:
The time taken by the block to return to the starting point is 1.2 s.
Explanation of Solution
Given:
The initial speed of the block
The angle of the incline
The speed of the block at the distance s is
Formula used:
The time taken by the crate to return to its starting point can be calculated using the third equation of motion.
Where,
Calculation:
When the block reaches the starting point, its net displacement snet is zero. Use 0 for s and the given values of v,
The equation has two roots,
Since
Conclusion:
The motion of a block sliding upthe inclined plane is analyzed by constructing its free body diagram. The acceleration of the block is determined using the free body diagram and Newton’s second law. Using the equations of motion, the time taken by the block to reach the starting point is found to be1.2 s.
Chapter 4 Solutions
Physics: Principles with Applications
Additional Science Textbook Solutions
College Physics
Modern Physics
College Physics: A Strategic Approach (3rd Edition)
University Physics Volume 1
Essential University Physics: Volume 1 (3rd Edition)
University Physics (14th Edition)
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON