DATA Figure P6.90 shows the results of measuring the force F exerted on both ends of a rubber band to stretch it a distance x from its unstretched position. (Source: www.scicnccboddics.org) The data points are well fit by the equation F = 33.55 x 0.4871 , where F is in newtons and x is in meters, (a) Does this rubber band obey Hooke’s law over the range of x shown in the graph? Explain, (b) The stiffness of a spring that obeys Hooke’s law is measured by the value of its force constant k . where k = F / x . This can be written as k = d F /d x to emphasize the quantities that are changing. Define k eff = d F /d x and calculate k eff as a function of x for this rubber band. For a spring that obeys Hooke’s law, k eff is constant, independent of x . Does the stiffness of this band, as measured by k eff , increase or decrease as x is increased, within the range of the data? (c) How much work must be done to stretch the rubber band from x = 0 to x = 0.0400 m? From x = 0.0400 m to x = 0.0800 m? (d) One end of the rubber band is attached to a stationary vertical rod, and the band is stretched horizontally 0.0800 m from its unstretched length. A 0.300-kg object on a horizontal, friction less surface is attached to the free end of the rubber band and released from rest. What is the speed of the object after it has traveled 0.0400 m?
DATA Figure P6.90 shows the results of measuring the force F exerted on both ends of a rubber band to stretch it a distance x from its unstretched position. (Source: www.scicnccboddics.org) The data points are well fit by the equation F = 33.55 x 0.4871 , where F is in newtons and x is in meters, (a) Does this rubber band obey Hooke’s law over the range of x shown in the graph? Explain, (b) The stiffness of a spring that obeys Hooke’s law is measured by the value of its force constant k . where k = F / x . This can be written as k = d F /d x to emphasize the quantities that are changing. Define k eff = d F /d x and calculate k eff as a function of x for this rubber band. For a spring that obeys Hooke’s law, k eff is constant, independent of x . Does the stiffness of this band, as measured by k eff , increase or decrease as x is increased, within the range of the data? (c) How much work must be done to stretch the rubber band from x = 0 to x = 0.0400 m? From x = 0.0400 m to x = 0.0800 m? (d) One end of the rubber band is attached to a stationary vertical rod, and the band is stretched horizontally 0.0800 m from its unstretched length. A 0.300-kg object on a horizontal, friction less surface is attached to the free end of the rubber band and released from rest. What is the speed of the object after it has traveled 0.0400 m?
DATA Figure P6.90 shows the results of measuring the force F exerted on both ends of a rubber band to stretch it a distance x from its unstretched position. (Source: www.scicnccboddics.org) The data points are well fit by the equation F = 33.55x0.4871, where F is in newtons and x is in meters, (a) Does this rubber band obey Hooke’s law over the range of x shown in the graph? Explain, (b) The stiffness of a spring that obeys Hooke’s law is measured by the value of its force constant k. where k = F/x. This can be written as k = dF/dx to emphasize the quantities that are changing. Define keff = dF/dx and calculate keff as a function of x for this rubber band. For a spring that obeys Hooke’s law, keff is constant, independent of x. Does the stiffness of this band, as measured by keff, increase or decrease as x is increased, within the range of the data? (c) How much work must be done to stretch the rubber band from x = 0 to x = 0.0400 m? From x = 0.0400 m to x = 0.0800 m? (d) One end of the rubber band is attached to a stationary vertical rod, and the band is stretched horizontally 0.0800 m from its unstretched length. A 0.300-kg object on a horizontal, friction less surface is attached to the free end of the rubber band and released from rest. What is the speed of the object after it has traveled 0.0400 m?
A ball is thrown with an initial speed v, at an angle 6, with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/4. In terms of R and g, find the following.
(a) the time interval during which the ball is in motion
2R
(b) the ball's speed at the peak of its path
v=
Rg 2
√ sin 26, V 3
(c) the initial vertical component of its velocity
Rg
sin ei
sin 20
(d) its initial speed
Rg
√ sin 20
×
(e) the angle 6, expressed in terms of arctan of a fraction.
1
(f) Suppose the ball is thrown at the same initial speed found in (d) but at the angle appropriate for reaching the greatest height that it can. Find this height.
hmax
R2
(g) Suppose the ball is thrown at the same initial speed but at the angle for greatest possible range. Find this maximum horizontal range.
Xmax
R√3
2
An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once before reaching the catcher. Assume the angle at which the bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in the figure, but that the ball's speed after the bounce is one-half of what it was before the bounce.
8
(a) Assuming the ball is always thrown with the same initial speed, at what angle & should the fielder throw the ball to make it go the same distance D with one bounce (blue path) as a ball thrown upward at 35.0° with no bounce (green path)?
24
(b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw.
Cone-bounce
no-bounce
0.940
Chapter 6 Solutions
University Physics with Modern Physics, Books a la Carte Plus Mastering Physics with eText -- Access Card Package (14th Edition)
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.
Work and Energy - Physics 101 / AP Physics 1 Review with Dianna Cowern; Author: Physics Girl;https://www.youtube.com/watch?v=rKwK06stPS8;License: Standard YouTube License, CC-BY