PHYS 212 FOR SCI+ENG W/MAST PHYS >ICP<
PHYS 212 FOR SCI+ENG W/MAST PHYS >ICP<
1st Edition
ISBN: 9781323834831
Author: Knight
Publisher: PEARSON C
bartleby

Videos

Textbook Question
Book Icon
Chapter 4, Problem 1CQ

a. At this instant, is the particle in FIGURE Q4.1 speeding up, slowing down, or traveling at constant speed?
b. Is this particle curving to the right, curving to the left, or traveling straight?

a.

Expert Solution
Check Mark
To determine

The state of the particle: speeding up, slowing down or traveling at constant speed.

Answer to Problem 1CQ

Solution:

The particle is slowing down in the vertical axis and speeding up in the horizontal axis.

Explanation of Solution

The acceleration vector has a component that it is pointing in the opposite direction to velocity vector; this means the particle will slow down on this axis. The component in the horizontal axis will make the particle to speed up.

Given Info:

There is a constant speed vector at the vertical axis and a constant acceleration vector with a component at both axes.

Formula Used The particle has the next velocity vector equation:

  velocity=(vx,o+ax,0t)x̂+(vy,o+ay,0t)ŷ

Where:

  ax,0=a.cosθ

It is negative because it is pointing to the left.

  ay,0=a.sinθ

It is negative because it is pointing downward.

  vy,0=v

  vx,0=0

Where a and v are the magnitudes of acceleration and velocity vector respectively.

Calculation

Substituting these values in the equation of velocity vector:

  velocity=(a.cosθt)x̂+(va.sinθt)ŷ

Conclusion

As we can see in the equation of velocity vector, the horizontal component is continuously increasing in the negative direction and the vertical component is slowing down since the initial velocity vector and the component of the acceleration vector are pointing in opposite directions.

b.

Expert Solution
Check Mark
To determine

The shape of the particle trajectory.

Answer to Problem 1CQ

Solution:

The particle curves to the left.

Explanation of Solution

Given Info:

There is a constant speed vector at the vertical axis and a constant acceleration vector with a component at both axes.

Every second, the velocity vector changes the position vector as well as the acceleration vector changes the velocity direction and magnitude. As we can see the acceleration vector is partially pointing to the left, therefore the velocity vector will be changing in that direction and so the position vector.

Formula We can obtain the position equation from the previous problem:

                            velocity=(a.cosθt)x̂+(va.sinθt)ŷ

  position=(a.cosθt)x̂+(va.sinθt)ŷ dt

  position=(12a.cosθt2)x̂+(vt12a.sinθt2)ŷ

Calculation

We can graph the last equation, and assuming the values:

  |v|=1[ms],          |a|=0.5[ms2],          θ=40°

  PHYS 212 FOR SCI+ENG W/MAST PHYS >ICP<, Chapter 4, Problem 1CQ

Conclusion

As we can see, the particle trajectory curves to the left because the acceleration vector has a component on the horizontal axis which points the same way.

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!
06:07
Students have asked these similar questions
1. a. At this instant, is the particle in FIGURE Q4.10 speeding up, slowing down, or traveling at constant speed? FIGURE Q4.1 a or traveling straight? V b. Is this particle curving to the right, curving to the left,
You wish to row straight across a 63-m-wide river. You can row at a steady 1.3 m/s relative to the water, and the river flows at 0.57 m/s A. In what direction should you head? Express your answer using two significant figures. B. How long will it take you to cross the river? Express your answer using two significant figures.
You throw a ball toward a wall at speed 25.0 m/s and at angle 00 = 40.3° above the horizontal. The wall is distance d =24.3 m from the release point of the ball. a. How far above the release point does the ball hit the wall? b. What are the horizontal and vertical components of its velocity as it hits the wall? c. When it hits, has it passed the highest point on its Trajectory?

Chapter 4 Solutions

PHYS 212 FOR SCI+ENG W/MAST PHYS >ICP<

Ch. 4 - II. In FIGURE Q4.11. Yvette and Zack are driving...Ch. 4 - In uniform circular motion, which of the following...Ch. 4 - FIGURE Q4.13 shows three points on a steadily...Ch. 4 - FIGURE Q4.14 shows four rotating wheels. For each,...Ch. 4 - FIGURE Q4.15 shows a pendulum at one end point of...Ch. 4 - Problems I and 2 show a partial motion diagram....Ch. 4 - Prob. 2EAPCh. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - A rocket-powered hockey puck moves on a horizontal...Ch. 4 - A rocket-powered hockey puck moves on a horizontal...Ch. 4 - Prob. 8EAPCh. 4 - A particle moving in the xy- plane has velocity v...Ch. 4 - You have a remote-controlled car that has been...Ch. 4 - A ball thrown horizontally at 25 m/s travels a...Ch. 4 - A physics student on the Planet Exidor throws a...Ch. 4 - A supply plane needs to drop a package of food to...Ch. 4 - A rifle is aimed horizontally at a target 50 m...Ch. 4 - In the Olympic shotput event, an athlete throws...Ch. 4 - On the Apollo 14 mission to the moon, astronaut...Ch. 4 - A baseball player friend of yours wants to...Ch. 4 - A boat takes 3.0 hours to travel 30 km down a...Ch. 4 - When the moving sidewalk at the airport is broken,...Ch. 4 - Prob. 20EAPCh. 4 - A kayaker, needs to paddle north across a...Ch. 4 - Susan, driving north at 60 mph, and Trent, driving...Ch. 4 - FIGURE EX4.23 shows the...Ch. 4 - FIGURE EX4.24 shows the...Ch. 4 - FIGURE EX4.25 shows the...Ch. 4 - The earth’s radius is about 4000 miles. Kampala,...Ch. 4 - An old-fashioned single-play vinyl record rotates...Ch. 4 - As the earth mates, what is the speed of (a) a...Ch. 4 - How fast must a plane fly along the earth’s...Ch. 4 - A 3000-rn-high mountain is located on the equator....Ch. 4 - Peregrine falcons are known for their maneuvering...Ch. 4 - To withstand “g-forces” of up to 10 g’s, caused by...Ch. 4 - The radius of the earth’s very nearly circular...Ch. 4 - A speck of dust on a spinning DVD has a...Ch. 4 - Your roommate is working on his bicycle and has...Ch. 4 - I FIGURE EX4.36 shows the angular velocity graph...Ch. 4 - I FIGURE EX4.37 shows the angular acceleration...Ch. 4 - FIGURE EX4.38 shows the...Ch. 4 - A wheel initially rotating at 60 rpm experiences...Ch. 4 - A 5.0-rn-diameter merry-go-round is initially...Ch. 4 - An electric fan goes from rest to 1800 rpm in 4.0...Ch. 4 - A bicycle wheel is rotating at 50 rpm when the...Ch. 4 - Starting from rest, a DVD steadily accelerates to...Ch. 4 - A spaceship maneuvering near Planet Zeta is...Ch. 4 - equation reference goes here45. A particle moving...Ch. 4 - A projectile’s horizontal range over level ground...Ch. 4 - a. A projectile is launched with speed v0and angle...Ch. 4 - A projectile is launched from ground level at...Ch. 4 - A gray kangaroo can bound across level ground with...Ch. 4 - A ball is thrown toward a cliff of height h with a...Ch. 4 - A tennis player hits a ball 2.0 m above the...Ch. 4 - You are target shooting using a toy gun that fires...Ch. 4 - A 35 g steel ball is held by a ceiling-mounted...Ch. 4 - You are watching an archery tournament when you...Ch. 4 - You’re 6.0 m from one wall of the house seen in...Ch. 4 - Sand moves without slipping at 6.0 m/s down a...Ch. 4 - A stunt man drives a car at a speed of 20 m/s off...Ch. 4 - A javelin thrower standing at rest holds the...Ch. 4 - A rubber ball is dropped onto a ramp that is...Ch. 4 - You are asked to consult for the city’s research...Ch. 4 - Ships A and B leave port together. For the next...Ch. 4 - While driving north at 25 m/s during a rainstorm...Ch. 4 - You’ve been assigned the task of using a shaft...Ch. 4 - Prob. 64EAPCh. 4 - Prob. 65EAPCh. 4 - Astronauts use a centrifuge to simulate the...Ch. 4 - Communications satellites are placed in a circular...Ch. 4 - Prob. 68EAPCh. 4 - A high-speed drill rotating ccw at 2400 rpm comes...Ch. 4 - A turbine is spinning at 3800 rpm. Frication in...Ch. 4 - Prob. 71EAPCh. 4 - The angular velocity of a process control motor is...Ch. 4 - A Ferris wheel of radius R speeds up with angular...Ch. 4 - Prob. 74EAPCh. 4 - A painted tooth on a spinning gear has angular...Ch. 4 - A car starts from rest on a curve with radius of...Ch. 4 - Prob. 77EAPCh. 4 - In Problem 78 through 80 you are given the...Ch. 4 - Prob. 79EAPCh. 4 - In Problem 78 through 80 you are given the...Ch. 4 - In one contest at the country fair, seen in FIGURE...Ch. 4 - Prob. 82EAPCh. 4 - Prob. 83EAPCh. 4 - Prob. 84EAPCh. 4 - Prob. 85EAP
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
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Vectors and 2D Motion: Crash Course Physics #4; Author: CrashCourse;https://www.youtube.com/watch?v=w3BhzYI6zXU;License: Standard YouTube License, CC-BY