Given that the space station is free of gravitational force, it is required that it spins an certain speed to acquire centripetal acceleration.
In this case, you want that the centripetal acceleration, Ac, equals g (gravitational acceleration on the earth), becasue this will cause a centripetal force equal to the weight on earth.
The formula for centripetal acceleration is Ac = [angular velocity]^2*R
where R = [1/2]50.0m = 25.0 m
Ac = 9.81 m/s^2
=> [angular velocity]^2 = Ac/R = 9.81m/s^2v/ 25.0m = 0.3924 (rad/s)^2
[angular velocity] = √(0.3924) rad/s = 0.63 rad/s
Answer: 0.63 rad/s
Answer:
The value of the centripetal forces are same.
Explanation:
Given:
The masses of the cars are same. The radii of the banked paths are same. The weight of an object on the moon is about one sixth of its weight on earth.
The expression for centripetal force is given by,
where, is the mass of the object, is the velocity of the object and is the radius of the path.
The value of the centripetal force depends on the mass of the object, not on its weight.
As both on moon and earth the velocity of the cars and the radii of the paths are same, so the centripetal forces are the same.
Answer:
(a) λ= 0.603m
(b) v= 50.8329
(c)
Explanation:
(a)The string is an open pipe and five loops indicates that the wave forms three complete cycle in the string.
A circle represents 1 wavelength. The loops occupy the whole length of the pipe, hence;
3λ = 1.81m
λ=
λ= 0.603m
(b) speed(v) = fλ
v= 84.3 * 0.603
v= 50.8329
(c) The string represents an open pipe.for an open pipe, the fundamental frequency is
Answer:
(A) The magnitude of the tension increases to four times its original value, 4F.
Explanation:
When an object moves in circular motion, a centripetal force acts on it . In this scenario the centripetal force acting on the stone is given by .
Where m is the mass of object
v- velocity or speed of the object
r - radius of the circle
Important to note is that the tension is equal to the centripetal force.
Given that initially the string makes one complete revolution per second and then speeds up to make two complete revolutions in a second .It implies that the speed has doubled .
Using our equation :F =
where F is the tension in the string
let the initial speed be =v then after it doubles it becomes 2v
Keeping the radius of the circle unchanged we have :
F=
From the equation it can be seen that the initial Tension has increased by a factor of 4 .
Therefore the magnitude of the tension increases to four times its original value, 4F.
<span>A wire carrying electric current will produce a magnetic field with closed field lines surrounding the wire.Another version of the right hand rules can be used to determine the magnetic field direction from a current—point the thumb in the direction of the current, and the fingers curl in the direction of the magnetic field loops created by it. See.<span>The Biot-Savart Law can be used to determine the magnetic field strength from a current segment. For the simple case of an infinite straight current-carrying wire it is reduced to the form <span><span>B=<span><span><span>μ0</span>I</span><span>2πr</span></span></span><span>B=<span><span><span>μ0</span>I</span><span>2πr</span></span></span></span>.</span><span>A more fundamental law than the Biot-Savart law is Ampere ‘s Law, which relates magnetic field and current in a general way. It is written in integral form as <span><span>∮B⋅dl=<span>μ0</span><span>Ienc</span></span><span>∮B⋅dl=<span>μ0</span><span>Ienc</span></span></span>, where Ienc is the enclosed current and μ0 is a constant.</span><span>A current-carrying wire feels a force in the presence of an external magnetic field. It is found to be <span><span>F=Bilsinθ</span><span>F=Bilsinθ</span></span>, where ℓ is the length of the wire, i is the current, and θ is the angle between the current direction and the magnetic field.</span></span>Key Terms<span><span>Biot-Savart Law: An equation that describes the magnetic field generated by an electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The law is valid in the magnetostatic approximation, and is consistent with both Ampère’s circuital law and Gauss’s law for magnetism.</span><span>Ampere’s Law: An equation that relates magnetic fields to electric currents that produce them. Using Ampere’s law, one can determine the magnetic field associated with a given current or current associated with a given magnetic field, providing there is no time changing electric field present.</span></span>