You are designing a simple elevator system for an old warehouse that is being converted to loft apartments. A 22.500-N elevator is to be accelerated upward by connecting it to a counter-weight by means of a light (but strong!) cable passing over a solid uniform disk-shaped pulley. The cable does not slip where it is in contact with the surface of the pulley. There is no appreciable friction at the axle of the pulley, but its mass is 875 kg and it is 1.50 m in diameter, (a) What mass should the counterweight have so that it will accelerate the elevator upward through 6.75 m in the first 3.00 s, starting from rest? (b) What is the tension in the cable on each side of the pulley? Figure P10.59
You are designing a simple elevator system for an old warehouse that is being converted to loft apartments. A 22.500-N elevator is to be accelerated upward by connecting it to a counter-weight by means of a light (but strong!) cable passing over a solid uniform disk-shaped pulley. The cable does not slip where it is in contact with the surface of the pulley. There is no appreciable friction at the axle of the pulley, but its mass is 875 kg and it is 1.50 m in diameter, (a) What mass should the counterweight have so that it will accelerate the elevator upward through 6.75 m in the first 3.00 s, starting from rest? (b) What is the tension in the cable on each side of the pulley? Figure P10.59
You are designing a simple elevator system for an old warehouse that is being converted to loft apartments. A 22.500-N elevator is to be accelerated upward by connecting it to a counter-weight by means of a light (but strong!) cable passing over a solid uniform disk-shaped pulley. The cable does not slip where it is in contact with the surface of the pulley. There is no appreciable friction at the axle of the pulley, but its mass is 875 kg and it is 1.50 m in diameter, (a) What mass should the counterweight have so that it will accelerate the elevator upward through 6.75 m in the first 3.00 s, starting from rest? (b) What is the tension in the cable on each side of the pulley?
In unit-vector notation, what is the net torque about the origin on a flea located at coordinates (0, 4.0 m, 5.0 m) when forces F 2 = (2.0 N)ˆj : AND 1 = (3.0 N)kˆ act on the flea?
Why is the following situation impossible? A uniform beam of mass mb = 3.00 kg and length ℓ = 1.00 m supports blocks with masses m1 = 5.00 kg and m2 = 15.0 kg at two positions as shown. The beam rests on two triangular blocks, with point P a distance d = 0.300 m to the right of the center of gravity of the beam. The position of the object of mass m2 is adjusted along the length of the beam until the normal force on the beam at O is zero.
A heavy swing door has a mass of
m = 8,000 kg,
a width
w = 1.0 m,
and a height
H = 3.9 m.
The door swings about a vertical axis passing through its center. The moment of inertia of this door about the vertical axis of rotation is given by
I =
1
12
mw2.
(a) You stand on one side and push at the outer edge of the door and perpendicular to the face of the door with a force of
F = 12.0 N.
Your friend pushes on the other outer edge of the door from the opposite side with the same force. What is the net torque, in N · m, applied to the door?
(b)What is the angular acceleration of the door in rad/s?
(c) Now consider a heavy door, with the same mass and dimensions as the one in part (a), that swings about a vertical axis passing through one long edge as shown in the diagram below. The moment of inertia of the door about this new axis of rotation is given by
I =
1
3
mw2,
where m is the mass and w is the width of the door.
How much force, in Newtons, must you…
Chapter 10 Solutions
University Physics with Modern Physics (14th Edition)
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