A ball is held at rest at some height above a horizontal surface. Once the ball is released at time t = 0, it falls under gravity, hits the surface at time t = T1 and starts bouncing up and down vertically. Suppose that with each bounce the ball loses a fixed fraction p of its energy (with 1>p>0). This loss could be due to a number of reasons (inelasticity, drag, etc) that are left unspecified. How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not simply a one-line answer. How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time Tstop? Give your answer for Tstop as a single formula that contains only two independent variables, namely the fractional energy loss p and the time T1 .

A ball is held at rest at some height above a horizontal surface. Once the ball is released at time t = 0, it falls under gravity, hits the surface at time t = T1 and starts bouncing up and down vertically. Suppose that with each bounce the ball loses a fixed fraction p of its energy (with 1>p>0). This loss could be due to a number of reasons (inelasticity, drag, etc) that are left unspecified. How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not simply a one-line answer. How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time Tstop? Give your answer for Tstop as a single formula that contains only two independent variables, namely the fractional energy loss p and the time T1 .

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 60P: Why is the following situation impossible? In a new casino, a supersized pinball machine is...

See similar textbooks

Similar questions

Why 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.
A 1000 kg spacecraft is approaching Jupiter (which is at the origin). The position of the spacecraft is given by the vector RSC = (0.0,-2.533) x 106km. The velocity is given by VSC= (+6.00, +8.00) km/sec. The mass of Jupiter, (MJ=318 MEarth) and MEarth = 5.97 x 1024 kg. A) What is the potential and kinetic energy of the spacecraft (write each to 3 sig figs.) What is the total energy of the spacecraft? Call the total energy Ei. B) Can it escape Jupiter? Justify your answer. C) What is the angular momentum of the spacecraft around Jupiter? Call this Li.
a pendulum of length L= 1.25 m. Its bob (which effectively has all the mass) has speed v0 when the cord makes an angle u0 =40.0 with the vertical. (a) What is the speed of the bob when it is in its lowest position if v0 = 8.00 m/s? What is the least value that v0 can have if the pendulum is to swing down and then up (b) to a horizontal position, and (c) to a vertical position with the cord remaining straight? (d) Do the answers to (b) and (c) increase, decrease, or remain the same if u0 is increased by a few degrees?
consider a popgun with a spring constant 843 N/m. A projectile of mass 0.06 kg is inserted into the barrel of the gun, and the spring is compressed 0.03 m. The gun is fired directly upward. Neglect any frictional forces or air resistance. What do they find is the maximum height of the projectile? What do they find is the highest speed of the projectile?
A mass M1 (of 2.5 kg) slides without friction on a table at a speed of 5 m/sec towards a mass M2 of 5 kg which can also slide without friction on the table. There is a spring on the face of M2 that will contact M1. If the spring constant is 100 N/m, what will be the maximum compression of the spring?
A stuntman of mass 55 kg is to be launched horizontally out of a spring- loaded cannon. The spring that will launch the stuntman has a spring coefficient of 266 N/m and is compressed 5 m prior to launching the stuntman. If friction and air resistance can be ignored, what will be the approximate velocity of the stuntman once he has left the cannon? A. 4 m/s B. 7 m/s C. 11 m/s D. 15 m/s
A spring with a fixed spring of K=200 (N/m) was attached to an object of M=8 (kg), which is stagnant on a horizontal ground without friction. An object of m=2 (kg) with the Mcismi shown in the figure is held with the spring x=0.8 (m). How much(m/s) is the speed of mass M when the system is released?
If a system consist of 5 particles, how many terms appear in the expression for total potential energy ? A) 5 B)10 C)15 D)20
Three objects with masses m1= 2.0 kg, m2= 4.0 kg, and m3= 6.0 kg, respectively, are attached by strings over frictionless pulleys as indicated in the figure. Assume the coefficient of kinetic friction between m2 and the tabletop is 0.25 and the system is released from rest. What is the speed of m3 after it falls 1.5 m?
A girl throws a ball at an inclined wall from a height of 3 ft, hitting the wall at A with a horizontal velocity v0 of magnitude 25 ft/s. Knowing that the coefficient of restitution between the ball and the wall is 0.9 and neglecting friction, determine the distance d from the foot of the wall to the point B where the ball will hit the ground after bouncing off the wall.
Two pole-vaulters just clear the bar at the same height. The first lands at a speed of 8.06 m/s, while the second lands at a speed of 8.41 m/s. The first vaulter clears the bar at a speed of 1.23 m/s. Ignore air resistance and friction and determine the speed at which the second vaulter clears the bar.
A 7.7 kg mass is attached to a massless spring with spring constant k = 32.7 n/m . The system rests on a frictionless horizontal surface. If the spring is compressed by 8.6 cm, then released, what is the maximum velocity of the mass?