CALC A block with mass m is revolving with linear speed υ 1 in a circle of radius r 1 on a frictionless horizontal surface (see Fig. E10.40). The string is slowly pulled from below until the radius of the circle in which the block is revolving is reduced to r 2 . (a) Calculate the tension T in the string as a function of r , the distance of the block from the hole. Your answer will be in terms of the initial velocity υ 1 and the radius r 1 . (b) Use W = ∫ r 1 r 2 T → ( r ) • d r → to calculate the work done by T → when r changes from r 1 to r 2 . (c) Compare the results of part (b) to the change in the kinetic energy of the block.
CALC A block with mass m is revolving with linear speed υ 1 in a circle of radius r 1 on a frictionless horizontal surface (see Fig. E10.40). The string is slowly pulled from below until the radius of the circle in which the block is revolving is reduced to r 2 . (a) Calculate the tension T in the string as a function of r , the distance of the block from the hole. Your answer will be in terms of the initial velocity υ 1 and the radius r 1 . (b) Use W = ∫ r 1 r 2 T → ( r ) • d r → to calculate the work done by T → when r changes from r 1 to r 2 . (c) Compare the results of part (b) to the change in the kinetic energy of the block.
CALC A block with mass m is revolving with linear speed υ1 in a circle of radius r1 on a frictionless horizontal surface (see Fig. E10.40). The string is slowly pulled from below until the radius of the circle in which the block is revolving is reduced to r2. (a) Calculate the tension T in the string as a function of r, the distance of the block from the hole. Your answer will be in terms of the initial velocity υ1 and the radius r1. (b) Use
W
=
∫
r
1
r
2
T
→
(
r
)
•
d
r
→
to calculate the work done by
T
→
when r changes from r1 to r2. (c) Compare the results of part (b) to the change in the kinetic energy of the block.
Thor flies by spinning his hammer really fast from a leather strap at the end of the handle, letting go, then grabbing it and having it pull him. If Thor wants to reach escape velocity (velocity needed to leave Earth’s atmosphere), he will need the linear velocity of the center of mass of the hammer to be 11,200 m/s. Thor's escape velocity is 33532.9 rad/s, the angular velocity is 8055.5 rad/s^2. While the hammer is spinning at its maximum speed what impossibly large tension does the leather strap, which the hammer is spinning by, exert when the hammer is at its lowest point? the hammer has a total mass of 20.0kg.
If the room’s radius is 16.2 m, at what minimum linear speed does Quicksilver need to run to stay on the walls without sliding down? Assume the coefficient of friction between Quicksilver and the wall is 0.236.
In the comics Thor flies by spinning his hammer really fast from a leather strap at the end of the handle, letting go, then grabbing it and having it pull him. If Thor wants to reach escape velocity (velocity needed to leave Earth’s atmosphere), he will need the linear velocity of the center of mass of the hammer to be 11,200 m/s. A) If the distance from the end of the strap to the center of the hammer is 0.334 m, what angular velocity does Thor need to spin his hammer at to reach escape velocity? b) If the hammer starts from rest what angular acceleration does Thor need to reach that angular velocity in 4.16 s? c) While the hammer is spinning at its maximum speed what impossibly large tension does the leather strap, which the hammer is spinning by, exert when the hammer is at its lowest point? The hammer has a total mass of 20.0kg.
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