Assume the resistive force acting on a speed skater is proportional to the square of the skater’s speed v and is given by f = −kmv2, where k is a constant and m is the skater’s mass. The skater crosses the finish line of a straight-line race with speed vi and then slows down by coasting on his skates. Show that the skater’s speed at any time t after crossing the finish line is v(t) = vi/(1 + ktvi).
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Physics for Scientists and Engineers with Modern Physics
Additional Science Textbook Solutions
Conceptual Physics (12th Edition)
The Physics of Everyday Phenomena
Lecture- Tutorials for Introductory Astronomy
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
Physics for Scientists and Engineers, Technology Update (No access codes included)
Sears And Zemansky's University Physics With Modern Physics
- A block with mass m1 hangs from a rope that is extended over an ideal pulley and attached to a second block with mass m2 that sits on a ledge. The second block is also connected to a third block with mass m3 by a second rope that hangs over a second ideal pulley as shown in Figure P5.47. If the friction between the ledge and the second block is negligible, m1 = 3.00 kg, m2 = 5.00 kg, and m3 = 8.00 kg, find the magnitude of the tension in each rope and the acceleration of each block. FIGURE P5.47arrow_forwardA particle of mass m slides down an inclined plane under the influence of gravity. If the motion is resisted by a force f = kmυ2, show that the time required to move a distance d after starting from rest is where θ is the angle of inclination of the plane.arrow_forwardA 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.arrow_forward
- A block of mass 144 kg lies on a horizontal plane. A horizontal force F of magnitude 1100 N is applied to the block causing it to move 3.25 meters. If the coefficient of friction between the block and the horizontal surface is 0.39, find the velocity (in m/s) of the block. Round off only on the final answer expressed in 3 decimal places. Use g = 9.81 m/s2arrow_forwardA girl of mass m1=60.0 kilograms springs from a trampoline with an initial upward velocity of vi=8.00 meters per second. At height h=2.00 meters above the trampoline, the girl grabs a box of mass m2=15.0 kilograms. For this problem, use g=9.80 meters per second per second for the magnitude of the acceleration due to gravity. What is the speed vbefore of the girl immediately before she grabs the box? What is the speed vafter of the girl immediately after she grabs the box? What is the maximum height hmax that the girl (with box) reaches? Measure hmax with respect to the top of the trampoline?arrow_forwardTwo penguins, Wheezy and Mumble, are racing down an icy slope into the water below. Wheezy has a mass of 22 kg. Mumble has a mass of 25 kg. The slope is angled at eight degrees to the horizontal. They both start from the same position at the same time, and slide down the icy slope entirely due to gravity alone. There is a coefficient of kinetic friction of 0.12 between the penguins and the ice. Who wins the race and what is the winner's acceleration when they reach the finish line (ie the water)?arrow_forward
- As a protest against the umpire's calls, a baseball pitcher throws a ball straight up into the air at a speed of 19.5 m/s. In the process, he moves his hand through a distance of 1.55 m. If the ball has a mass of 0.150 kg, find the force he exerts on the ball to give it this upward speed.arrow_forwardA particle of mass 1.05 kg is subject to a force that is always pointed towards the East but whose magnitude changes linearly with time t. The magnitude of the force is given as F = 4t, and has units of newtons. Let the x-axis point towards the East. Determine the change in x-coordinate in meters of the particle Δx between t = 0 and t = 2.4 if the initial velocity is 17.5 m/s, and pointed in the same direction as the force.arrow_forwardA constant horizontal force F = 200 N is applied for a time 0.1 s by a kick to a soccer ball of mass m=0.4 kg. If the ball was initially traveling toward the player at 20 m/s, what is the speed as it leaves her foot traveling in the opposite direction? Choose the correct answer. 50 m/s 20 m/s 10 m/s 30 m/s 70 m/sarrow_forward
- A 10-kg box initially at rest is pulled to the right along a frictionless horizontal surface by a horizontal force of 60N, determine the speed of the box after it has moved 2.0 m. r=4.89 m/sarrow_forwardDuring a ski competition, a skier moves on a track ABOC situated in a vertical plane as shown in the adjacent figure. The skier, starts from A from rest, he descends on AB in a uniformly accelerated rectilinear motion, and reaches B with a speed of 22 m/s. The duration of motion of the skier between A and B is 9.67 s. Given: AB is inclined by an angle a = 22° with respect to the horizontal. The mass of the skier: m = 80 kg. g = 9.8 m/s. 1)Calculate the acceleration of the skier on AB and the distance AB. 2)Applying Newton's second law, calculate the force of friction acting on the skier during its downward motion on AB. 3)At the point 0, the skier becomes air born, at t = 0, with a speed Ve = 21 m/s making an angle B = 50° with the horizontal. Neglect air resistance. a)Determine, in the system (xOy) of the figure, the parametric equations of motion of the center of inertia of the skier. Deduce the equation of his trajectory. b)Determine the coordinates of the point of impact I of…arrow_forwardA wooden ball of weight 196 newtons is dropped vertically from a height of 100 meters above the ground. Throughout the fall, drag is present by a factor 4v due to air resistance, where v is the velocity of the ball at time t (in seconds). After how many seconds will the ball impact the ground? Assume that the net force acting on the ball is modeled by m(dv/dt) = mg – kv, where m is the mass of the ball. Also, assume that there is no initial velocity and that the acceleration due to gravity g is 9.8 meters per second squared. Do not round off intermediate steps. Round off the final answer to two decimal places.arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning