Answer:
a) 0 Nm b) mgL/2 Nm counterclockwise
Explanation:
Before we even begin answering the question, we have to appreciate the fact that the weight of the constant density symmetrical rigid objects is considered to be acting from its geometrical center, which we will call the center of mass. If the clock arm is considered to be rectangular , rigid and constant density(assumed, since this is a high school question) we can proceed with our analysis. We also note that the torque on the arm are given by,
where m is the total mass of the arm , x is the horizontal distance(perpendicular to the direction of force) of the center of mass of the arm from the center of the clock and g is the acceleration due to gravity. Also let L be the length of the hour arm.
In part a) the horizontal distance of the center of mass of the arm from the center of the clock would be zero since at noon the center of mass of the clock arm is right above the center of the clock. So x = 0 , hence T = 0 Nm.
in part b) the horizontal distance between the center of mass of the arm and the center of the clock is L/2 , where L is the length of the hour arm , but the weight acts from half that distance since the weight of the object is considered to be acting from the geometrical center of the object which in this case is L/2 distance away from the center of the clock. So plugging into the above equation we get T = mg*(L/2) Nm, the force acting downwards from the left since the arm is pointing at 9:00 , which will result in a counter clockwise torque. So T=mgL/2 Nm counter clockwise is the Torque due to the hour arm.
If you already know calculus you can check the answer to part b) by evaluating the integral,
where M is the mass per unit length of the arm. m is the total mass given by m=ML.
Answer:
Actually, Polaris, also named alpha Ursa Minoris, is the brightest star in the Little Dipper. It marks the end of the handle. By a twist of luck, it also happens to reside very close to the North Celestial Pole (NCP). This is the point in the sky that all the stars in the north rotate around. It’s not exactly on the NCP, in fact it’s more than a Moons width away, so it scribes out a very small circle in long exposure star trail images like this one below. To the unaided eye it appears that all the stars rotate around Polaris while it remains fixed in one spot. During the last half of the 20th century Polaris’ variations had dropped to approximately 2%. No other Cepheid is known to have gone through this. Astronomers believed they were witnessing the evolution of the star before their very eyes, and that eventually we would see Polaris’ variations snuff out entirely.
Explanation:
Answer:
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Explanation:
Torque is equal to force times distance. first calculate the weight of the 8-0 kg weight, using the formula:
F = mg
where g is the accelration due to gravity ( 9.81 m/s^2)
F = 8 kg ( 9.81 m / s^2 )
F = 78.48 N
and torque = Fl
where l is the distance
t = (78.48 N ) ( 0.55 m )
t = 43.16 Nm is the torque
Answer:
True
Explanation:
Its faster the way the machine does it