(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?
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
 alt="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?
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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
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