EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
16th Edition
ISBN: 8220100546716
Author: Katz
Publisher: CENGAGE L
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 2, Problem 76PQ

Two carts are set in motion at t = 0 on a frictionless track in a physics laboratory. The first cart is launched from an initial position of x = 18.0 cm with an initial velocity of 11.8î cm/s and a constant acceleration of –3.40î cm/s2. The second cart is launched from x = 20.0 cm with a constant velocity of 4.30î cm/s.

  1. a. N What are the times for which the two carts have equal speeds?
  2. b. N What are the speeds of the carts at that time?
  3. c. N What are the locations and times at which the carts pass each other?
  4. d. C What is the difference between what is asked in parts (a) and (c) of this problem with regard to the times you found?

(a)

Expert Solution
Check Mark
To determine

Time at which two carts moves with same speed.

Answer to Problem 76PQ

Time at which two carts moves with same speed will be 2.21s.

Explanation of Solution

Write the Newton’s equation for velocity for the first cart.

    v1=u1+a1t

Here, v1 is the final velocity of first cart, u1 is the initial velocity of first cart, a1 is the acceleration of first cart, and t is the time taken.

Write the Newton’s equation for velocity for the second cart.

    v2=u2+a2t

Here, v2 is the final velocity of second cart, u2 is the initial velocity of second cart, and a2 is the acceleration of second cart.

Equate the right hand sides’ of above equations.

    u1+a1t=u2+a2t

Rewrite the above equation in terms of t.

    t=u2u1a1a2

Conclusion:

Substitute 4.30cm/s for u2, 11.8cm/s for u1, 3.40cm/s2 for a2, and 0cm/s2 in the above equation to find t.

  t=4.30cm/s11.8cm/s3.40cm/s20cm/s2=2.21s

Therefore, the time at which two carts moves with same speed will be 2.21s.

(b)

Expert Solution
Check Mark
To determine

Speed of carts at that time.

Answer to Problem 76PQ

Both carts will be at the speed of 4.30cm/s.

Explanation of Solution

It is given that the first cart is only accelerating. Second one is moving at fixed velocity, 4.30cm/s. So when both carts will be at equal speeds, means that the first cart also achieved the speed 4.30cm/s.

Therefore, both carts will be at the speed of 4.30cm/s.

(c)

Expert Solution
Check Mark
To determine

The position and time when the carts pass each other.

Answer to Problem 76PQ

The time is 0.285sand 4.13s and the corresponding positions are 21.2cmand 37.7cm respectively.

Explanation of Solution

Write the Newton’s equation for displacement of first cart.

    x1f=x1i+u1t+12a1t2

Here, x1f is the final position of first car and x1i is the initial position of car.

Write the Newton’s equation for displacement of first cart.

    x2f=x2i+u2t+12a2t2

Here, x2f is the final position of second cart and x2i is the initial position of second cart.

Equate the right hand sides of above two equations.

  x1i+u1t+12a1t2=x2i+u2t+12a2t2

Conclusion:

Substitute 18.0cm for x1i, 11.8cm/s for u1, 3.40cm/s2 for a1, 20.0cm for x2i, 0cm/s2 for a2, 4.30cm/s for u2 in the above equation to find t.

  18cm+(11.8cm/s)t+12(3.40cm/s2)t2=20.0cm+(4.30cm/s)t+12(0cm/s2)t218cm+(11.8cm/s)t12(3.40cm/s2)t2=20.0cm+(4.30cm/s)t36cm+(23.6cm/s)t(3.40cm/s2)t2=40.0cm+(8.60cm/s)t(3.40cm/s2)t2(15.0cm/s)t+4.0cm=0

Divide the above equation by 2.

    (1.70cm/s2)t2(7.50cm/s)t+2.0cm=0

Rewrite the above equation in terms of t

    t=(7.50cm/s)±(7.50cm/s)24(1.70cm/s2)2.0cm2(1.70cm/s2)=4.13sor0.285s

Substitute 18.0cm for x1i, 11.8cm/s for u1, 3.40cm/s2 for a1, and 0.285s for t in the equation for x1f to find the position of cart at 0.285s.

    v1f=18cm+(11.8cm/s)(0.285s)+12(3.40cm/s2)(0.285s)2=21.36cm0.16cm=21.2cm

Substitute 18.0cm for x1i, 11.8cm/s for u1, 3.40cm/s2 for a1, and 4.13s for t in the equation for x1f to find the position of cart at 4.13s.

  v1f=18cm+(11.8cm/s)(4.13s)+12(3.40cm/s2)(4.13s)2=66.73cm29.03cm=37.7cm

Therefore, the time is 0.285sand 4.13s and the corresponding positions are 21.2cmand 37.7cm respectively.

(d)

Expert Solution
Check Mark
To determine

The difference in meaning of question in part (a) and part (b).

Answer to Problem 76PQ

Part (a) asks to find the instant at which carts having same speed and part (b) asks to identify the time at carts will be at the same position.

Explanation of Solution

In part (a), it is asked to find the time at which both carts having the same speed and in part (b), it is asked to find the time at which both carts are at the same location.

From the starting point to a moment just before 0.285s, first car was moving behind the second car. But it was on acceleration. So at 0.285s, first car passes the second car. At this point, both cars will at different velocity. After 0.285s, first car starts decreasing its speed. So at 4.13s, two cars came together once more. Between 0.285s and 4.13s, at 2.21s, velocity of cars became same.

Therefore, part (a) asks to find the instant at which carts having same speed and part (b) asks to identify the time at carts will be at the same position.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
No chatgpt pls will upvote
a cubic foot of argon at 20 degrees celsius is isentropically compressed from 1 atm to 425 KPa. What is the new temperature and density?
Calculate the variance of the calculated accelerations. The free fall height was 1753 mm. The measured release and catch times were:  222.22 800.00 61.11 641.67 0.00 588.89 11.11 588.89 8.33 588.89 11.11 588.89 5.56 586.11 2.78 583.33   Give in the answer window the calculated repeated experiment variance in m/s2.

Chapter 2 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

Ch. 2 - Prob. 4PQCh. 2 - For each of the following velocity vectors, give...Ch. 2 - In the traditional Hansel and Gretel fable, the...Ch. 2 - After a long and grueling race, two cadets, A and...Ch. 2 - Prob. 8PQCh. 2 - Elisha Graves Otis invented the elevator brake in...Ch. 2 - As shown in Figure 2.9, Whipple chose a coordinate...Ch. 2 - Prob. 11PQCh. 2 - Prob. 12PQCh. 2 - A race car travels 825 km around a circular sprint...Ch. 2 - Prob. 14PQCh. 2 - A train leaving Albuquerque travels 293 miles, due...Ch. 2 - Prob. 16PQCh. 2 - The position of a particle attached to a vertical...Ch. 2 - Prob. 18PQCh. 2 - Prob. 19PQCh. 2 - Prob. 20PQCh. 2 - During a relay race, you run the first leg of the...Ch. 2 - Prob. 22PQCh. 2 - Prob. 23PQCh. 2 - Prob. 24PQCh. 2 - During a thunderstorm, a frightened child is...Ch. 2 - Scientists and engineers must interpret problems...Ch. 2 - Prob. 27PQCh. 2 - Prob. 28PQCh. 2 - A In attempting to break one of his many swimming...Ch. 2 - A The instantaneous speed of a particle moving...Ch. 2 - A particles velocity is given by vy(t)=atj, where...Ch. 2 - Prob. 32PQCh. 2 - Figure P2.33 shows the y-position (in blue) of a...Ch. 2 - A particles position is given by z(t) = (7.50...Ch. 2 - Prob. 35PQCh. 2 - Two sprinters start a race along a straight track...Ch. 2 - An electronic line judge camera captures the...Ch. 2 - During a bungee jump, a student (i) initially...Ch. 2 - Prob. 39PQCh. 2 - Prob. 40PQCh. 2 - Prob. 41PQCh. 2 - Prob. 42PQCh. 2 - Prob. 43PQCh. 2 - Prob. 44PQCh. 2 - A computer system, using a preset coordinate...Ch. 2 - In Example 2.6, we considered a simple model for a...Ch. 2 - A uniformly accelerating rocket is found to have a...Ch. 2 - Prob. 48PQCh. 2 - A driver uniformly accelerates his car such that...Ch. 2 - Car A and car B travel in the same direction along...Ch. 2 - Accelerating uniformly to overtake a slow-moving...Ch. 2 - An object that moves in one dimension has the...Ch. 2 - A particle moves along the positive x axis with a...Ch. 2 - Case Study Crall and Whipple attached a fan to a...Ch. 2 - Prob. 55PQCh. 2 - The engineer of an intercity train observes a rock...Ch. 2 - A pebble is thrown downward from a 44.0-m-high...Ch. 2 - In a cartoon program, Peter tosses his baby,...Ch. 2 - Tadeh launches a model rocket straight up from his...Ch. 2 - Prob. 60PQCh. 2 - In the movie Star Wars: The Empire Strikes Back,...Ch. 2 - A worker tosses bricks one by one to a coworker on...Ch. 2 - A rock is thrown straight up into the air with an...Ch. 2 - Prob. 64PQCh. 2 - A sounding rocket, launched vertically upward with...Ch. 2 - Prob. 66PQCh. 2 - While strolling downtown on a Saturday Afternoon,...Ch. 2 - Prob. 68PQCh. 2 - A trooper is moving due south along the freeway at...Ch. 2 - A dancer moves in one dimension back and forth...Ch. 2 - The electrical impulse initiated by the nerves in...Ch. 2 - Two cars leave Seattle at the same time en route...Ch. 2 - An object begins to move along the y axis and its...Ch. 2 - Prob. 74PQCh. 2 - Prob. 75PQCh. 2 - Two carts are set in motion at t = 0 on a...Ch. 2 - Prob. 77PQCh. 2 - Cars A and B each move to the right with constant...Ch. 2 - Prob. 79PQCh. 2 - Prob. 80PQCh. 2 - Prob. 82PQCh. 2 - Prob. 83PQCh. 2 - A Write expressions for the average acceleration...Ch. 2 - Prob. 85PQCh. 2 - Prob. 86PQCh. 2 - In 1898, the world land speed record was set by...Ch. 2 - In Example 2.12, two circus performers rehearse a...Ch. 2 - Prob. 89PQ
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Text book image
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill
Text book image
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
Position/Velocity/Acceleration Part 1: Definitions; Author: Professor Dave explains;https://www.youtube.com/watch?v=4dCrkp8qgLU;License: Standard YouTube License, CC-BY