Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
4th Edition
ISBN: 9780134110684
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 6, Problem 74EAP
A spring-loaded toy gun exerts a variable force on a plastic ball as the spring expands. Consider a horizontal spring and a ball of mass m whose position when barely touching a fully expanded spring is x = 0. The ball is pushed to the left, compressing the spring. You'll learn in Chapter 9 that the spring force on the ball, when the ball is at position x (which is negative), can be written as (Fsp)x= -kx, where k is called the spring constant. The minus sign is needed to make the x-component of the force positive. Suppose the ball is initially pushed to x0= -L, then released and shot to the right.
a. Use what you've learned in calculus to prove that
b. Find an expression, in terms of m, k, and L, for the speed of the ball as it comes off the spring at x = 0.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A spring-loaded toy gun exerts a variable force on a plastic ball as the spring expands. Consider a horizontal spring and a ball of mass m whose position when barely touching a fully expanded spring is x = 0. The ball is pushed to the left, compressing the spring. You'll learn in Chapter 9 that the spring force on the ball, when the ball is at position x (which is negative), can be written as (FSp)x=−kx , where k is called the spring constant. The minus sign is needed to make the x-component of the force positive. Suppose the ball is initially pushed to x0=−L, then released and shot to the right.
Find an expression, in terms of m, k, and L, for the speed of the ball as it comes off the spring x = 0.
Express your answer in terms of some or all of the variables m, k, and L.
An M = 22.4 kg sled slides on a rough horizontal ground. The sled hits a spring when it is traveling with a horizontal velocity of vi = 12.3 m/s. The sled compresses the spring at a distance of x = 2.12 m before coming to rest. If the force constant of the spring is k = 550 N/m, find the effective coefficient of kinetic friction, μk, between the sled and the ground
A mass of 0.5 kg moving with a speed of 1.5 m/s on
a horizontal smooth surface, collides with a nearly
weightless spring of force constant k = 50 N/m. The
maximum compression of the spring would be
Fooooo
Chapter 6 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 6 - Are the objects described here in equilibrium...Ch. 6 - A ball tosses straight up has v = 0 at its highest...Ch. 6 - Kat, Matt, and Nat are arguing about why a physics...Ch. 6 - If you know all of the forces acting on a moving...Ch. 6 - An elevator, hanging from a single cable, moves...Ch. 6 - An elevator, hanging from a single cable, moves...Ch. 6 - Are the following statements true or false?...Ch. 6 -
8. An astronaut takes his bathroom scale to the...Ch. 6 -
9. The four balls in FIGURE Q6.9 have been...Ch. 6 - Prob. 10CQ
Ch. 6 - Prob. 11CQCh. 6 - A hand presses down on the book in FIGURE Q6.12....Ch. 6 - Boxes A and B in FIGURES Q6.13 both remain at...Ch. 6 - Suppose you push a hockey puck of mass m across...Ch. 6 - A block pushed along the floor with velocity...Ch. 6 - A crate of fragile dishes is in the back of a...Ch. 6 - Five balls move through the air as shown in FIGURE...Ch. 6 - The three ropes in FIGURE EX6.1 are tied to a...Ch. 6 - The three ropes in FIGURE EX6.2 are tied to a...Ch. 6 - A football coach sits on a sled while two of his...Ch. 6 - A 20 kg loudspeaker is suspended 2.0 m below the...Ch. 6 - A 65 kg gymnast wedges himself between two closely...Ch. 6 - A construction worker with a weight of 850 N...Ch. 6 - In an electricity experiment, a 1.0 g plastic ball...Ch. 6 - The forces in FIGURE EX6.8 act on a 2.0 kg object....Ch. 6 - The forces in FIGURE EX6.9 act on a 2.0 kg object....Ch. 6 - FIGURE EX6.10 shows the velocity graph of a 2.0 kg...Ch. 6 - FIGURE EX6.11 shows the force acting on a 2.0 kg...Ch. 6 - A horizontal rope is tied to a 50 kg box on...Ch. 6 - A 50 kg box hangs from a rope. What is the tension...Ch. 6 - A 2.0 × 107 kg train applies its brakes with the...Ch. 6 - A 8.0 × 104 kg spaceship is at rest in deep space....Ch. 6 - The position of a 2.0 kg mass is given by x = (2t3...Ch. 6 - A woman has mass of 55 kg. a. What is her weight...Ch. 6 - It takes the elevator in a skyscraper 4.0 s to...Ch. 6 - Zach, whose mass is 80 kg, is in an elevator...Ch. 6 - What thrust does a 200 g model rocket need in...Ch. 6 - What thrust does a 200 g model rocket need in...Ch. 6 - A 20,000 kg rocket has a rocket motor that...Ch. 6 - The earth is 1.50 × 1011 m from the sun. The...Ch. 6 - Bonnie and Clyde are sliding a 300 kg bank safe...Ch. 6 - A stubborn, 120 kg mule sits down and refuses to...Ch. 6 - A 10 kg crate is placed on a horizontal conveyor...Ch. 6 - Bob is pulling a 30 kg filing cabinet with a force...Ch. 6 - A rubber-wheeled kg cart rolls down a 15° concrete...Ch. 6 - A 4000 kg truck is parked on a 15° slope. How big...Ch. 6 - A 1500 kg car skids to a halt on a wet road where...Ch. 6 - A 50,000 kg locomotive is traveling at 10 m/s when...Ch. 6 - You and your friend Peter are putting new shingles...Ch. 6 - An Airbus A320 jetliner has a takeoff mass of...Ch. 6 -
34. A medium-sized jet has a 3.8-m-diameter...Ch. 6 - A 75 kg skydiver can be modeled as a rectangular...Ch. 6 - A 6.5-cm-diameter ball has a terminal speed of 26...Ch. 6 - A 2.0 kg object initially at rest at the origin is...Ch. 6 - A 5.0 kg object initially at rest at the origin is...Ch. 6 - The 1000 kg steel beam in FIGURE P6.39 is...Ch. 6 - Henry, whose mass is 95 kg, stands on a bathroom...Ch. 6 - An accident victim with a broken leg is being...Ch. 6 - Seat belts and air bags save lives by reducing the...Ch. 6 - The piston of a machine exerts a constant force on...Ch. 6 - Compressed air is used to fire a 50 g ball...Ch. 6 - a. A rocket of mass m is launched straight up with...Ch. 6 - A rifle with a barrel length of 60 cm fires a 10 g...Ch. 6 - A truck with a heavy load has a total mass of 7500...Ch. 6 - An object of mass m is at rest at the top of a...Ch. 6 - Prob. 49EAPCh. 6 - A baggage handler drops your 10 kg suitcase onto a...Ch. 6 - A 2.0 kg wood block is launched up a wooden ramp...Ch. 6 - It’s a snowy day and you're pulling a friend along...Ch. 6 - A large box of mass M is pulled across a...Ch. 6 - Prob. 54EAPCh. 6 - You're driving along at 25 m/s with your aunt's...Ch. 6 - The 2.0 kg wood box in FIGURE P6.56 slides down a...Ch. 6 - A 1.0 kg wood block is pressed against a vertical...Ch. 6 - A person with compromised pinch strength in his...Ch. 6 - A ball is shot from a compressed-air gun at twice...Ch. 6 - Starting from rest, a 2500 kg helicopter...Ch. 6 - Astronauts in space "weigh" themselves by...Ch. 6 - A particle of mass m moving along the x-axis...Ch. 6 - At t = 0, an object of mass m is at rest at x = 0...Ch. 6 - At t = 0, an object of mass m is at rest at x = 0...Ch. 6 - Prob. 65EAPCh. 6 - A 60 kg skater is gliding across frictionless ice...Ch. 6 - Prob. 67EAPCh. 6 - Problems 68 and 69 show a free-body diagram. For...Ch. 6 - Problems 68 and 69 show a free-body diagram. For...Ch. 6 - Prob. 70EAPCh. 6 - In Problems 70 through 72 you are given the...Ch. 6 - In Problems 70 through 72 you are given the...Ch. 6 - A block of mass m is at rest at the origin at t =...Ch. 6 - A spring-loaded toy gun exerts a variable force on...Ch. 6 - FIGURE CP6.7S shows an accelerometer, a device for...Ch. 6 - An object moving in a liquid experiences a linear...Ch. 6 - Prob. 77EAPCh. 6 - An object with cross section A is shot...
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
- Assume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the bow back 50 cm and holds it in position with a force of 150 N. If the mass of the arrow is 50 g and the “spring” is massless, what is the speed of the arrow immediately after it leaves the bow?arrow_forwardWhy is the following situation impossible? In a new casino, a supersized pinball machine is introduced. Casino advertising boasts that a professional basketball player can lie on top of the machine and his head and feet will not hang off the edge! The ball launcher in the machine sends metal balls up one side of the machine and then into play. The spring in the launcher (Fig. P6.60) has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined = 10.0 with respect to the horizontal. The spring is initially compressed its maximum distance d = 5.00 cm. A ball of mass 100 g is projected into play by releasing the plunger. Casino visitors find the play of the giant machine quite exciting.arrow_forwardWhy is the following situation impossible? In a new casino, a supersized pinball machine is introduced. Casino advertising boasts that a professional basketball player can lie on top of the machine and his head and feet will not hang off the edge! The hall launcher in the machine sends metal halls up one side of the machine and then into play. The spring in the launcher (Fig. P7.44) has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined = 10.0 with respect to the horizontal. The spring is initially compressed its maximum distance d = 5.00 cm. A ball of mass 100 g is projected into play by releasing the plunger. Casino visitors find the play of the giant machine quite exciting. Figure P7.44arrow_forward
- A 6 000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in Figure P6.27 (page 188). Both springs are described by Hookes law and have spring constants k1 = 1 600 N/m and k2, = 3 400 N/m. After the first spring compresses a distance of 30.0 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 50.0 cm after first contacting the two-spring system. Find the cars initial speed.arrow_forwardAn athlete jumping vertically on a trampoline leaves the surface with a velocity of 8.5 m/s upward. What maximum height does she reach? (a) 13 m (b) 2.3 m (c) 3.7 m (d) 0.27 m (e) The answer cant be determined because the mass of the athlete isnt given.arrow_forwardTwo figure skaters are coasting in the same direction, with the leading skater moving at 5.5 m/s and the trailing skating moving at 6.2 m/s. When the trailing skater catches up with the leading skater, he picks her up without applying any horizontal forces on his skates. If the trailing skater is 50 heavier than the 50-kg leading skater, what is their speed after he picks her up?arrow_forward
- A 500 g particle has velocity vx = -8.0 m/s at t =-2 s. Force Fx=(4−t^2)N, where t is in s, is exerted on the particle between t=−2s and t = 2 s. This force increases from 0 N at t = -2 s to 4 N at t = 0 s and then back to 0 N at t = 2 s. What is the particle's velocity at t=2 s?arrow_forwardAssume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the drawstring back 70 cm from its rest position and holds it in position with a force of 160 N. If the mass of the arrow is 55 g and the "spring" is massless, what is the speed (in m/s) of the arrow immediately after it leaves the bow? 40 X m/sarrow_forwardA man pushing a crate of mass m = 92.0 kg at a speed of v = 0.860 m/s encounters a rough horizontal surface of length ℓ = 0.65 m as in the figure below. If the coefficient of kinetic friction between the crate and rough surface is 0.360 and he exerts a constant horizontal force of 279 N on the crate. A man pushes a crate labeled m, which moves with a velocity vector v to the right, on a horizontal surface. The horizontal surface is textured from the right edge of the crate to a horizontal distance ℓ from the right edge of the crate. (a) Find the magnitude and direction of the net force on the crate while it is on the rough surface. magnitude N direction (b) Find the net work done on the crate while it is on the rough surface. J(c) Find the speed of the crate when it reaches the end of the rough surface. m/sarrow_forward
- Assume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the drawstring back 62 cm from its rest position and holds it in position with a force of 170 N. If the mass of the arrow is 59 g and the "spring" is massless, what is the speed (in m/s) of the arrow immediately after it leaves the bow?arrow_forwardA 100 g particle moving along the x-axis experiences the force shown in (Figure 1). The particle's velocity is 2.0 m/s at x = 0 m. Figure Fx (N) 15 10 5 0 x (m) 0 1 2 3 1 of 1arrow_forwardThe 1.1 kgkg physics book in figure is connected by a string to a 550 gg coffee cup. The book is given a push up the slope and released with a speed of 2.9 m/sm/s . The coefficients of friction are μsμs =0.50=0.50 and μkμk =0.20=0.20.(Figure 1) How far does the book slide? Express your answer with the appropriate units.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Newton's Second Law of Motion: F = ma; Author: Professor Dave explains;https://www.youtube.com/watch?v=xzA6IBWUEDE;License: Standard YouTube License, CC-BY