College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
Question
Transcribed Image Text:### Problem Statement
The figure shows an overhead view of a 0.029 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table.
- Force \( \vec{F}_1 \) has a magnitude of 8 N and is at \( \theta_1 = 27^\circ \).
- Force \( \vec{F}_2 \) has a magnitude of 10 N and is at \( \theta_2 = 30^\circ \).
In unit-vector notation, what is the third force if the lemon half:
(a) is stationary,
(b) has the constant velocity \( \vec{v} = (12\hat{i} - 12\hat{j}) \) m/s,
(c) has the velocity \( \vec{v} = (14t\hat{i} - 15t\hat{j}) \) m/s², where t is time?
### Diagram Description
The diagram features a yellow circle representing the lemon half at the origin of an x-y coordinate system with two forces acting on it.
- The first force \( \vec{F}_1 \) is represented by a vector pointing upwards and slightly to the left, forming an angle \( \theta_1 \) of 27 degrees with the positive x-axis.
- The second force \( \vec{F}_2 \) is represented by a vector pointing downwards and to the right, forming an angle \( \theta_2 \) of 30 degrees with the positive x-axis.
### Input Fields for Solutions
**(a)** Force \( \vec{F}_3 \) if the lemon half is stationary:
- \( \text{Number} \) i + \( \text{Number} \) j \( \text{Units} \)
**(b)** Force \( \vec{F}_3 \) if the lemon half has constant velocity \( \vec{v} = (12\hat{i} - 12\hat{j}) \) m/s:
- \( \text{Number} \) i + \( \text{Number} \) j \( \text{Units} \)
**(c)** Force \( \vec{F}_3 \) if the lemon half has a velocity \( \vec{v} = (14t\hat{i} - 15t\hat{j}) \) m/s
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 5 steps with 7 images
Knowledge Booster
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
- Two constant forces act on an object of mass m = 4.30 kg object moving in the xy plane as shown in the figure below. Force F, is 26.5 N at 35.0°, and force F, is 48.0 N at 150°. At time t = 0, the object is at the origin and has velocity (3.50î + 2.15j) m/s. 150° 35.0° (a) Express the two forces in unit-vector notation. F, - N (b) Find the total force exerted on the object. N (c) Find the object's acceleration. m/s2 Now, consider the instant t = 3.00 s. (d) Find the object's velocity. m/s (e) Find its position. (f) Find its kinetic energy from V½mv2. kJ (g) Find its kinetic energy from 2mv,2 + EF · AF. kJarrow_forwardA constant horizontal force pushes a 7.50 kg FedEx package across a frictionless floor on which an xy coordinate system has been drawn. The figure gives the package's x and y velocity components versus time t. What are the (a) magnitude and (b) direction of F? Give the direction as a positive or negative angle of magnitude less than 180° relative to the +x-axis. Vy (m/s) v (m/s) x 10 5 (a) Number (b) Number 1 a 2 Units Units t (s) 3 0 -5 -10 IL 0 ◄► 3 t(s)arrow_forwardIn the figure, a crate of mass m = 94 kg is pushed at a constant speed up a frictionless ramp (0 = 31°) by a horizontal force F. The positive direction of an x axis is up the ramp, and the positive direction of a y axis is perpendicular to the ramp. (a) What is the magnitude of F? (b) What is the magnitude of the normal force on the crate? (a) Number Units (b) Number i Units >arrow_forward
- In the figure, a crate of mass m = 83 kg is pushed at a constant speed up a frictionless ramp (0 = 28°) by a horizontal force F.The positive direction of an x axis is up the ramp, and the positive direction of a y axis is perpendicular to the ramp. (a) What is the magnitude of F? (b) What is the magnitude of the normal force on the crate? (a) Number i Units (b) Number i Unitsarrow_forwardThe following three force vectors act on a particle: F1 = 2i+3j, F2 = -li – 4j, and F3 = -li+lj. (Figure 1) Add the three vectors graphically and determine whether the sum of the forces equals zero.arrow_forwardTwo horizontal forces act on a 4.0 kg chopping block that can slide over a frictionless kitchen counter, which lies in an xy plane. One force is É = (9.1 N)i+ (9.5 N). Find the acceleration of the chopping block in unit-vector notation when the other force is (a) F2=(-9.1 N)i+ (-9.5 N)ĵ, (b) F 1 = (-9.1 N)î + (9.5 N)3, and (e) F, = (9.1 N) î + (-9.5 N). 2%= (a) Number Units 1 Units (b) Number Units (c) Numberarrow_forward
- Three forces act on a moving object. One force has a magnitude of 75.0 N and is directed due north. Another has a magnitude of 54.6 N and is directed due west. What must be (a) the magnitude and (b) the direction of the third force, such that the object continues to move with a constant velocity? Express your answer as a positive angle south of east. (a) Number i (b) Number Units Unitsarrow_forwardThe figure shows an overhead view of a 0.022 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force F, has a magnitude of 8 N and is at 0₁-32. Force has a magnitude of 9 N and is at 02-25°. In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity=(141 - 113) m/s, and (c) has the 7 = (10ri - 11r)) m/s², where t is time? (a) Number 1 (b) Number i (c) Number i i+ i + H F KO 0 P F₂ X j Units j Units j Units >arrow_forwardThe figure shows an overhead view of a 0.025 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force F has a magnitude of 7 N and is at e, 29'. Force F has a magnitude of 9 N and is at 02-26". In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity = (127 - 16j) m/s, and (c) has the V = (14f- 13) m/s?, where t is time? %3D (a) Number -0.01 i+ 3.94 įUnits (b) Number -0.01 i+ 3.94 jUnits (c) Number 0.31 i+ 3.61 jUnitsarrow_forward
- A mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point, that is, F∝ r3, if the distance from the P to the position of the particle is r. It has been determined that the constant of proportionality is 0.23 N/m3, i.e. the magnitude of the force on a particle can be written as 0.23r3, when the particle is at a distance r from the force center. Find the magnitude of the potential energy, in joules, of a particle subjected to this force when the particle is at a distance 0.21 m from point P assuming the potential energy to be zero when the particle is at P. PE= ?arrow_forwardDetermine the force Q-> when the block moves with constant velocity. Express your answer in vector form.arrow_forwardIn the figure, a crate of mass m = 99 kg is pushed at a constant speed up a frictionless ramp (0 = 30°) by a horizontal force . The positive direction of an x axis is up the ramp, and the positive direction of a y axis is perpendicular to the ramp. (a) What is the magnitude of F? (b) What is the magnitude of the normal force on the crate? (a) Number i (b) Number Units Units II ATTIT This answer has no units °(degrees) m kgarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction 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 Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON