Concept explainers
The physics of circular motion sets an upper limit to the speed of human walking. (If you need to go faster, your gait changes from a walk to a run.) If you take a few steps and watch what’s happening, you’ll see that your body pivots in circular motion over your forward foot as you bring your rear foot forward for the next step. As you do so, the normal force of the ground on your foot decreases and your body tries to “lift off’ from the ground.
a. A person’s center of mass is very near the hips, at the top of the legs. Model a person as a particle of mass m at the top of a leg of length L. Find an expression for the person’s maximum walking speed vmax.
b. Evaluate your expression for the maximum walking speed of a 70 kg person with a typical leg length of 70 cm. Give your answer in both m/s and mph, then comment, based on your experience, as to whether this is a reasonable result. A “normal” walking speed is about 3 mph.
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
- A 670 N student stands in the middle of a frozen pond having a radius of 6.9 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 2.9 kg physics textbook horizontally toward the north shore at a speed of 6.9 m/s. The acceleration of gravity is 9.81 m/s². How long does it take him to reach the south shore? Answer in units of s.arrow_forwardKinesiologists—scientists who study human motion—can measure the forces that act on runners as they round a curve. The forces on a runner’s feet are a vertical normal force that, on average, serves to counteract gravity, and a static friction force parallel to the ground and pointing toward the center of the runner’s circular path. The average value of this inward-pointing force is measured to be 600 N for a 75 kg runner rounding a curve that has a 2.5 m radius. What is this runner’s speed?arrow_forwardSuppose you are at a bowling alley, where a machine uses a constant force and pushes balls up a ramp one meter in length. The balls are sliding -- not rolling -- along the incline, and they end up half a meter above the base of the ramp. Ignore friction. Approximately how much force does the machine put on a 5 kg bowling ball? 1.0 m H 0.5 m 200 N 50 N 25 N O 5N Impossible to determinearrow_forward
- In an amusement park water slide, people slide down an essentially frictionless tube. The top of the slide is 3.0 m above the bottom where they exit the slide, moving horizontally, 1.2 m above a swimming pool. What horizontal distance do they travel from the exit point before hitting the water? Does the mass of the person make any difference?arrow_forwardConsider a 25-kg block on a frictionless inclined plane held in place by a steel cable as shown in the figure. The cable is parallel to the surface of the incline. What is the magnitude of the tension on the steel cable? 25 kg 30° 212 N O 245 N O none of the choices O 123 N O 458 Narrow_forwardScientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 7.6-kg projectile from rest to a speed of 5.1 × 103 m/s. The net force accelerating the projectile is 6.4 × 105 N. How much time is required for the projectile to come up to speed?arrow_forward
- A 10 kg box is being pushed across a rough surface with a constant speed of 2 m/s. The person pushing the box slips and stops pushing. The box continues to slide across the surface before coming to rest. If the coefficient of friction between the crate and the surface is 0.1, how far does the box travel before coming to rest?arrow_forwardA constant force acting on a body of mass 3.0 kg changes its speed from 2.0 ms-1 to 3.5 ms-1 in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force?arrow_forwardA stacked pair of books with masses m1= 2.0 kg (bottom book) and m2 = 1.5 kg (top book) are tossed onto a table. The books strike the table with no vertical velocity and their common horizontal speed is ?o = 0.75 m/s. The kinetic friction coefficient between the bottom book and the table is ?k1=0.45; the kinetic and static friction coefficients between the two books are ?k2=0.3 and ?s2= 0.4. Find the final horizontal position of each book relative to the spot where the stack hits the table.arrow_forward
- A robot with fancy wheels is trained to move in two directions simultaneously. The force in the forward direction is 10 N and the force in the horizontal direction is 8 N. If the robot starts from rest, has a mass of 75 kg and travels for 100 seconds, what is the magnitude of the robot's final displacement?arrow_forwardA 5.0 g coin is placed 15 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of μs = 0.70 and μk = 0.50. The turntable very slowly speeds up. What is the frequency of the rotation of the turntable expressed in revolutions per minute when the coin slides off? Express your answer in revolutions per minute.arrow_forwardGrab a meter stick or any uniform thin piece of wood about 1m in length. (e.g. the handle of a broom with the head removed). Place your index fingers at either end so that you are holding the stick up with just two fingers. Move your fingers slowly together. Where do they end up? Describe the motion of your fingers. Explain why this happens.arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction 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 LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON