DATA A mass m is attached to a spring of force constant 75 N/m and allowed to oscillate. Figure P14.89 shows a graph of its velocity component v x as a function of time t . Find (a) the period, (b) the frequency, and (c) the angular frequency of this motion. (d) What is the amplitude (in cm), and at what times does the mass reach this position? (e) Find the maximum acceleration magnitude of the mass and the times at which it occurs. (f) What is the value of m ? Figure P14.89
DATA A mass m is attached to a spring of force constant 75 N/m and allowed to oscillate. Figure P14.89 shows a graph of its velocity component v x as a function of time t . Find (a) the period, (b) the frequency, and (c) the angular frequency of this motion. (d) What is the amplitude (in cm), and at what times does the mass reach this position? (e) Find the maximum acceleration magnitude of the mass and the times at which it occurs. (f) What is the value of m ? Figure P14.89
DATA A mass m is attached to a spring of force constant 75 N/m and allowed to oscillate. Figure P14.89 shows a graph of its velocity component vx as a function of time t. Find (a) the period, (b) the frequency, and (c) the angular frequency of this motion. (d) What is the amplitude (in cm), and at what times does the mass reach this position? (e) Find the maximum acceleration magnitude of the mass and the times at which it occurs. (f) What is the value of 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
A rocket is launched at an angle of 60.0° above the horizontal with an initial speed of 97 m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 28.0 m/s². At this time, its engines fail and the rocket proceeds to move as a projectile.
(a) Find the maximum altitude reached by the rocket.
1445.46
Your response differs from the correct answer by more than 10%. Double check your calculations. m
(b) Find its total time of flight.
36.16
x
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. s
(c) Find its horizontal range.
1753.12
×
Your response differs from the correct answer by more than 10%. Double check your calculations. m
Chapter 14 Solutions
Mastering Physics with Pearson eText -- Standalone Access Card -- for University Physics with Modern Physics (14th Edition)
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