Concept explainers
(a)
Speed of first particle before collision.
(a)
Explanation of Solution
Given:
Particle of mass
The particles stick together after collision.
Formula used:
Write the expression of total energy of particle
Here,
Write the expression of total energy in terms of gamma factor
Here,
Substitute
Simplify the above expression for
Write the expression of gamma factor
Here,
Simplify above expression for
Calculation:
The value of
Substitute
Substitute 3 for
Conclusion:
Thus, the speed of first particle before collision is
(b)
Total energy of first particle before collision.
(b)
Explanation of Solution
Given:
Particle of mass
The particles stick together after collision.
Formula used:
Write the expression of total energy of particle
Here,
Calculation:
Substitute 3 for
Conclusion:
Thus, the total energy of first particle before collision is
(c)
Initial total momentum of system.
(c)
Explanation of Solution
Given:
Particle of mass
The particles stick together after collision.
Formula used:
Write the expression of the total relativistic energy
Here,
Rearrange the above expression
Calculation:
Substitute
Conclusion:
Thus, the initial total momentum of system is
(d)
Total kinetic energy after collision.
(d)
Explanation of Solution
Given:
Particle of mass
The particles stick together after collision.
Formula used:
Since the total energy is conserved during collision therefore
Here,
Since the momentum is conserved during the collision therefore
Here,
Write the expression for rest mass energy
Write the expression for total kinetic energy
Calculation:
Substitute
Substitute
Conclusion:
Thus, the total kinetic energy after collision is
(e)
Mass of system after collision.
(e)
Explanation of Solution
Given:
Particle of mass
The particles stick together after collision.
Formula used:
Write the expression of mass of system
Here, is mass of the system after collision
Calculation:
Substitute
Conclusion:
Thus, the mass of system after collision is
Want to see more full solutions like this?
Chapter 39 Solutions
Physics for Scientists and Engineers
- An enemy spacecraft moves away from the Earth at a speed of v = 0.800c (Fig. P9.19). A galactic patrol spacecraft pursues at a speed of u = 0.900c relative to the Earth. Observers on the Earth measure the patrol craft to be overtaking the enemy craft at a relative speed of 0.100c. With what speed is the patrol craft overtaking the enemy craft as measured by the patrol crafts crew? Figure. P9.19arrow_forwardTwo powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially 2.52 × 1012 m apart as measured by Liz, an Earth observer, as shown in Figure P1.34. Both rockets are 50.0 m in length as measured by Liz. (a) What are their respective proper lengths? (b) What is the length of each rocket as measured by an observer in the other rocket? (c) According to Liz, how long before the rockets collide? (d) According to rocket 1, how long before they collide? (e) According to rocket 2, how long before they collide? (f) If both rocket crews are capable of total evacuation within 90 min (their own time), will there be any casualties? Figure P1.34arrow_forwardOwen and Dina are at rest in frame S, which is moving at 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P9.63). Owen throws the ball to Dina at 0.800c (according to Owen), and their separation (measured in S) is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, (d) how fast is the ball moving, and (e) what time interval is required for the ball to reach Dina? Figure P9.63arrow_forward
- In a frame at rest with respect to the billiard table, a billiard ball of mass m moving with speed v strikes another billiard ball of mass m at rest. The first ball comes to rest after the collision while the second ball takes off with speed v in the original direction of the motion of the first ball. This shows that momentum is conserved in this frame. (a) Now, describe the same collision from the perspective of a frame that is moving with speed v in the direction of the motion of the first ball. (b) Is the momentum conserved in this frame?arrow_forwardAn unstable particle with mass m = 3.34 1027 kg is initially at rest. The particle decays into two fragments that fly off along the x axis with velocity components u1 = 0.987c and u2 = 0.868c. From this information, we wish to determine the masses of fragments 1 and 2. (a) Is the initial system of the unstable particle, which becomes the system of the two fragments, isolated or nonisolated? (b) Based on your answer to part (a), what two analysis models are appropriate for this situation? (c) Find the values of for the two fragments after the decay. (d) Using one of the analysis models in part (b), find a relationship between the masses m1 and m2 of the fragments. (e) Using the second analysis model in part (b). find a second relationship between the masses m1 and m2. (f) Solve the relationships in parts (d) and (c) simultaneously for the masses m1 and m2.arrow_forward(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.arrow_forward
- An atomic clock is placed in a jet airplane. The clock measures a time interval of 3600 s when the jet moves with a speed of 400 m/s. How much longer or shorter a time interval does an identical clock held by an observer on the ground measure? (Hint: For , γ ≈ 1 + v2/2c2.)arrow_forwardOwen and Dina are at rest in frame S, which is moving with a speed of 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P26.45). Owen throws the ball to Dina with a speed of 0.800c (according to Owen) and their separation (measured in S) is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, and (d) how fast is the ball moving? Figure. P26.45arrow_forwardOwen and Dina are at rest in frame S, which is moving with a speed of 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P26.45). Owen throws the ball to Dina with a speed of 0.800c (according to Owen) and their separation (measured in S) is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, and (d) how fast is the ball moving? Figure. P26.45arrow_forward
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning