(67) The spacecraft designers have decided that the 200-meter-radius spacecraft only needs to produce an acceleration of 0.5g. What speed will produce that acceleration?

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Chapter1: Units, Trigonometry. And Vectors
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can you do number 67 please.
SAMPLE PROBLEM
Artificial Gravity
A large, doughnut-shaped section of a spacecraft is being designed for long-term space
flight. The outer wall of the rotating section will become the floor for the astronauts, and
the centripetal acceleration produced by the floor will simulate gravity. If this section of the
spacecraft has a radius of 200.0 m, what speed will produce an acceleration of 9.81 m/s²?
1. DRAW A PICTURE Sketch a picture of
the situation.
3. PLAN AND EXECUTE Use mathematical relationships, the picture,
and your definitions to plan and execute a solution.
Write the equation for the centripetal
acceleration and solve for v².
46
2. DEFINE THE PROBLEM List knowns and
unknowns, and assign values to variables.
R = 200.0 m
V = ?
a = 9.81 m/s²
Take the square root of both sides to solve for v.
Determine the magnitude of the velocity.
GO ONLINE for more math support.
Math Practice Problems
a
4. EVALUATE Reflect on your answer.
The units are appropriate for velocity. The speed of rotation is
reasonable, about 160 kilometers per hour.
= →v² = a.R
v = √a R
y =
(9.81 m/s²) (200.0 m) = 44.3 m/s
aelpnaht
(67) The spacecraft designers have decided that the 200-meter-radius spacecraft
only needs to produce an acceleration of 0.5g. What speed will produce that
acceleration?
e embubong vol noit
NEED A HINT? Go online to your eText Sample Problem for stepped out support.
(68) A fairground ride spins its occupants inside a large teacup. If the radius of the
circular path is 10.0 m and the acceleration is 1.5g, what is the speed of the riders?
Investigation 1 Modeling Motion
Gre
The t
of po
An c
mov
usin
des
cor
Transcribed Image Text:SAMPLE PROBLEM Artificial Gravity A large, doughnut-shaped section of a spacecraft is being designed for long-term space flight. The outer wall of the rotating section will become the floor for the astronauts, and the centripetal acceleration produced by the floor will simulate gravity. If this section of the spacecraft has a radius of 200.0 m, what speed will produce an acceleration of 9.81 m/s²? 1. DRAW A PICTURE Sketch a picture of the situation. 3. PLAN AND EXECUTE Use mathematical relationships, the picture, and your definitions to plan and execute a solution. Write the equation for the centripetal acceleration and solve for v². 46 2. DEFINE THE PROBLEM List knowns and unknowns, and assign values to variables. R = 200.0 m V = ? a = 9.81 m/s² Take the square root of both sides to solve for v. Determine the magnitude of the velocity. GO ONLINE for more math support. Math Practice Problems a 4. EVALUATE Reflect on your answer. The units are appropriate for velocity. The speed of rotation is reasonable, about 160 kilometers per hour. = →v² = a.R v = √a R y = (9.81 m/s²) (200.0 m) = 44.3 m/s aelpnaht (67) The spacecraft designers have decided that the 200-meter-radius spacecraft only needs to produce an acceleration of 0.5g. What speed will produce that acceleration? e embubong vol noit NEED A HINT? Go online to your eText Sample Problem for stepped out support. (68) A fairground ride spins its occupants inside a large teacup. If the radius of the circular path is 10.0 m and the acceleration is 1.5g, what is the speed of the riders? Investigation 1 Modeling Motion Gre The t of po An c mov usin des cor
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