Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 2, Problem 2.54P
A potato of mass 0.5 kg moves under Earth’s gravity with an air resistive force of −kmv. (a) Find the terminal velocity if the potato is released from rest and k = 0.01 s−1. (b) Find the maximum height of the potato if it has the same value of k, but it is initially shot directly upward with a student-made potato gun with an initial velocity of 120 m/s.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A ball of mass m = 0.490 kg is dropped near the surface of the Earth.However, there exists an air resistance F = −βv, where β = 0.700 N · s/m. After a long time, the ballapproaches a speed v. What is this speed?
A ball of mass m is shot from a spring gun whose spring has a force constant k. The spring can be compressedΔx. How high can the ball be shot if the gun is aimed vertically? After you have an algebraic solution, let m = 15g, k = 600N/m and Δx = 5cm.
Consider an object of mass m = 4 kg on a frictionless table. The object experiences a repulsive force F = a/x2 + b/x, where F is in newtons and x is the position of the object relative to the origin.
If the object starts at rest at a position x3 = 1.3 m and is released, at what speed v, in meters per second, will the object be moving when it is at position x4 = 12.5 m?
Chapter 2 Solutions
Classical Dynamics of Particles and Systems
Ch. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - If a projectile is fired from the origin of the...Ch. 2 - A clown is juggling four balls simultaneously....Ch. 2 - A jet fighter pilot knows he is able to withstand...Ch. 2 -
In the blizzard of ’88, a rancher was forced to...Ch. 2 - Prob. 2.7PCh. 2 - A projectile is fired with a velocity 0 such that...Ch. 2 - Consider a projectile fired vertically in a...Ch. 2 - Prob. 2.11P
Ch. 2 - A particle is projected vertically upward in a...Ch. 2 -
A particle moves in a medium under the influence...Ch. 2 - A projectile is fired with initial speed 0 at an...Ch. 2 -
A particle of mass m slides down an inclined...Ch. 2 - A particle is projected with an initial velocity 0...Ch. 2 - A strong softball player smacks the ball at a...Ch. 2 - Prob. 2.19PCh. 2 - A gun fires a projectile of mass 10 kg of the type...Ch. 2 - Prob. 2.21PCh. 2 - Prob. 2.22PCh. 2 - A skier weighing 90 kg starts from rest down a...Ch. 2 - A block of mass m = 1.62 kg slides down a...Ch. 2 - A child slides a block of mass 2 kg along a slick...Ch. 2 - A rope having a total mass of 0.4 kg and total...Ch. 2 - A superball of mass M and a marble of mass m are...Ch. 2 - An automobile driver traveling down an 8% grade...Ch. 2 - A student drops a water-filled balloon from the...Ch. 2 - Prob. 2.31PCh. 2 - Two blocks of unequal mass are connected by a...Ch. 2 - A particle is released from rest (y = 0) and falls...Ch. 2 - Perform the numerical calculations of Example 2.7...Ch. 2 - Prob. 2.36PCh. 2 - A particle of mass m has speed υ = α/x, where x is...Ch. 2 - The speed of a particle of mass m varies with the...Ch. 2 - A boat with initial speed υ0 is launched on a...Ch. 2 - A train moves along the tracks at a constant speed...Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Consider a particle moving in the region x > 0...Ch. 2 - Prob. 2.48PCh. 2 - Prob. 2.49PCh. 2 - According to special relativity, a particle of...Ch. 2 - Let us make the (unrealistic) assumption that a...Ch. 2 - A particle of mass m moving in one dimension has...Ch. 2 - A potato of mass 0.5 kg moves under Earth’s...Ch. 2 - Prob. 2.55P
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
- A ball of mass m is shot from a spring gun whose spring has a force constant k. The spring can be compressed Δx. How high can the ball be shot if the gun is aimed vertically? After you have an algebraic solution, let m = 15g, k = 600N/m and Δx = 5cm.arrow_forwardThe boat is moving at 10 m/s when its engine is shutdown. Due to hydrodynamic drag, its subsequent acceleration is a = -0.05v^2 m/s^2 where v is the velocity of the boat in m/s. What is the boat’s velocity 4 s after the engine is shut down?arrow_forwardA child is sitting on a stationary skateboard with a pile of rocks which she throws in one direction in order to make the skateboard travel in the opposite direction. If the rocks each have a mass of 0.90 kg and she can throw them with a speed of 12 m/s relative to the ground, determine the number of rocks she must throw per minute in order to maintain a constant average speed against a 1.8 N force of friction. (Note: because this is a rate, the answer may not be a whole number.) rocks/min Enter a number.arrow_forward
- A box of mass m = 0.14 kg is set against a spring with a spring constant of kį = 670 N/m which has been compressed by a distance of 0.1 m. Some distance in front of it, along a frictionless surface, is another spring with a spring constant of k2 = 204 N/m. (a) How far, d, in meters, will the second spring compress when the box runs into it? (b) How fast, v in meters per second, will the box be moving when it strikes the second spring? (c) Now assume that the surface is rough (that is, not frictionless). You perform the experiment and observe| that the second spring only compresses a distance dy/2. How much energy, in joules, was lost to friction? marrow_forwardA 61.5-kg athlete leaps straight up into the air from a trampoline with an initial speed of 9.4 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? This answer has not been graded yet. (b) Select the height at which the athlete's speed is 9.4 m/s as y = 0. What is her kinetic energy at this point? What is the gravitational potential energy associated with the athlete? (c) What is her kinetic energy at maximum height? What is the gravitational potential energy associated with the athlete? (d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. (e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer. m/sarrow_forwardConsider a 3.2 kg block that is connected to the surface of the Earth with a vertical springthat has 760 N/m and a relaxed length of 2.2 m. Furthermore, the block is surrounded bya dense gas. At 0 s you pull the block to a height of 2.4 m and throw the block verticallydownward with a velocity of magnitude 6.6 m/s. The block first comes to momentaryrest at a height of 1.9 m.Write out a function for the amount of thermal energy that must be generated due toair resistance, and evaulate that function numerically.arrow_forward
- A 66.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 7.5 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? This answer has not been graded yet. (b) Select the height at which the athlete's speed is 7.5 m/s as y = 0. What is her kinetic energy at this point? JWhat is the gravitational potential energy associated with the athlete? J(c) What is her kinetic energy at maximum height? JWhat is the gravitational potential energy associated with the athlete? J(d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. m(e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer. m/sarrow_forwardTwo masses are pressed against opposite ends of a spring, with one mass at either end of the spring. The spring is has a spring constant of 181 N/m and the two 0.200 kg masses are identical to each other. Pressing the masses against the ends of the spring compresses the spring 21.5 cm from its normal length. If both masses rest on a frictionless, horizontal table, find the speed of each mass in SI units when it has moved free of the spring on the table.arrow_forward(b) A particle of unit mass moving in one dimension obeys the equation of motion x = (i) Show that i2 – e" is a constant of the motion. (ii) At t = 0 the particle is at x = 0 and at rest, i.e. x(0) = ¿(0) = 0. Show that the particle reaches x = +o at finite t > 0. Hint: use the result of part (i) to write the time taken to reach x = +0 as an integral. (iii) What is a suitable Lagrangian for this system?arrow_forward
- A 235 kg roller coaster is at the top of a hill with a velocity of 5.60 m/s from a height of 100.0 m above the ground. A) Determine the velocity of the roller coaster at a height of 40.0 m furtherdown the track, neglecting friction. B) What reference point did you choose as zero height? Show how you could come up with the same answer to A if you chose another reference point for height.arrow_forwardA particle of mass 1.06 kg begins at rest and is then subject to a force in the positive x direction that changes with time as given by the following function: F = mg[1-e-2.1t ], where g is the acceleration due to gravity. Part (a) Determine the change in the velocity Δv of the particle between t = 0 and t = 2.4 sec. Part (b) Determine the change in x-coordinate of the particle Δx between t = 0 and t = 2.4.arrow_forwardSolve the following: You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose spring constant is kk is suspended from the ceiling. A block of mass MM hangs from the spring. A bullet of mass mm is fired vertically upward into the bottom of the block. The spring's maximum compression dd is measured from its initial suspended position.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Mechanical work done (GCSE Physics); Author: Dr de Bruin's Classroom;https://www.youtube.com/watch?v=OapgRhYDMvw;License: Standard YouTube License, CC-BY