Water drives a waterwheel (or turbine) of radius R = 3.0 m as shown in Fig. 11–47. The water enters at a speed υ 1 = 7.0 m/s and exits from the waterwheel at a speed υ 2 = 3.8m/s. ( a ) If 85 kg of water passes through per second, what is the rate at which the water delivers angular momentum to the waterwheel? ( b ) What is the torque the water applies to the waterwheel? ( c ) If the water causes the waterwheel to make one revolution every 5.5 s, how much power is delivered to the wheel? FIGURE 11-47 Problem 73.
Water drives a waterwheel (or turbine) of radius R = 3.0 m as shown in Fig. 11–47. The water enters at a speed υ 1 = 7.0 m/s and exits from the waterwheel at a speed υ 2 = 3.8m/s. ( a ) If 85 kg of water passes through per second, what is the rate at which the water delivers angular momentum to the waterwheel? ( b ) What is the torque the water applies to the waterwheel? ( c ) If the water causes the waterwheel to make one revolution every 5.5 s, how much power is delivered to the wheel? FIGURE 11-47 Problem 73.
Water drives a waterwheel (or turbine) of radius R = 3.0 m as shown in Fig. 11–47. The water enters at a speed υ1 = 7.0 m/s and exits from the waterwheel at a speed υ2 = 3.8m/s. (a) If 85 kg of water passes through per second, what is the rate at which the water delivers angular momentum to the waterwheel? (b) What is the torque the water applies to the waterwheel? (c) If the water causes the waterwheel to make one revolution every 5.5 s, how much power is delivered to the wheel?
FIGURE 11-47
Problem 73.
Study of body parts and their functions. In this combined field of study, anatomy refers to studying the body structure of organisms, whereas physiology refers to their function.
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
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