Question

In: Physics

The cable lifting an elevator is wrapped around a 1.2-m-diameter cylinder that is turned by the...

The cable lifting an elevator is wrapped around a 1.2-m-diameter cylinder that is turned by the elevator's motor. The elevator is moving upward at a speed of 1.3 m/s . It then slows to a stop, while the cylinder turns one complete revolution.

How long does it take for the elevator to stop?

Solutions

Expert Solution

Diameter of the cylinder = D = 1.2 m

Radius of the cylinder = R = D/2 = 0.6 m

Speed of the elevator = V = 1.3 m/s

Initial angular speed of the cylinder = 1

V = 1R

1.3 = 1(0.6)

1 = 2.167 rad/s

Final angular speed of the cylinder = 2 = 0 rad/s (Comes to rest)

The cylinder makes 1 revolution before coming to rest.

Angle traveled by the cylinder = = 2 = 6.283 rad

Angular acceleration of the cylinder =

Time taken to come to a stop = T

22 = 12 + 2

(0)2 = (2.167)2 + 2(6.283)

= -0.373 rad/s2

2 = 1 + T

0 = 2.167 + (-0.373)T

T = 5.81 sec

Time taken by the elevator to come to a stop = 5.81 sec


Related Solutions

A cord is wrapped around a pulley of diameter 0.320 m with the free end tied...
A cord is wrapped around a pulley of diameter 0.320 m with the free end tied to a weight. That weight is allowed to descend at constant acceleration. A stopwatch is started at the instant when the weight reaches a speed of 0.023 m/s. At a time of t = 1.50 s, the weight has dropped an additional 0.080 m. Calculate the magnitude of the centripetal acceleration of any point on the circumference of the pulley at t = 4.0...
A rope of negligible mass is wrapped around a 225-kg solid cylinder of radius 0.400 m....
A rope of negligible mass is wrapped around a 225-kg solid cylinder of radius 0.400 m. The cylinder is suspended several meters off the ground with its axis oriented horizontally, and turns on that axis without friction. (a) If a 75.0-kg man takes hold of the free end of the rope and falls under the force of gravity, what is his acceleration? m/s2 (b) What is the angular acceleration of the cylinder? rad/s2 (c) If the mass of the rope...
String is wrapped around an object of mass M = 0.3 kg and moment of inertia...
String is wrapped around an object of mass M = 0.3 kg and moment of inertia I = 0.01 kg·m2. You pull the string with your hand straight up with some constant force F such that the center of the object does not move up or down, but the object spins faster and faster (see the figure). This is like a yo-yo; nothing but the vertical string touches the object. When your hand is a height y0 = 0.26 m...
A 580-mm long tungsten wire, with a 0.046-mm-diameter circular cross section, is wrapped around in the...
A 580-mm long tungsten wire, with a 0.046-mm-diameter circular cross section, is wrapped around in the shape of a coil and used as a filament in an incandescent light bulb. When the light bulb is connected to a battery, a current of 0.526 A is measured through the filament. (Note: tungsten has a resistivity of 4.9 × 10-8 ? • m.) How many electrons pass through this filament in 5 seconds? How many electrons pass through this filament in 5...
A high-speed lifting mechanism supports a 710 kg object with a steel cable 20.0 m long...
A high-speed lifting mechanism supports a 710 kg object with a steel cable 20.0 m long and 4.00 cm2 in cross-sectional area. (a) Determine the elongation of the cable. _____ mm (b) By what additional amount does the cable increase in length if the object is accelerated upward at a rate of 2.6 m/s2? _____ mm (c) What is the greatest mass that can be accelerated upward at 2.6 m/s2 if the stress in the cable is not to exceed...
A 1-m-diameter cylinder, 1 m long, is maintained at 800 K and has an emissivity of...
A 1-m-diameter cylinder, 1 m long, is maintained at 800 K and has an emissivity of 0.65. Another cylinder, 2 m in diameter and 1 m long, encloses the first cylinder and is perfectly insulated. Both cylinders are placed in a large room maintained at 300 K. Calculate the heat lost by the inner cylinder.
A disc with radius 0.060 m and rotational inertia 0.061 kg.m^2 has a rope wrapped around...
A disc with radius 0.060 m and rotational inertia 0.061 kg.m^2 has a rope wrapped around its parameter. The other end of the rope is holding a 0.20 kg mass. The mass is held at 1.0 m above the floor. You release the mass from rest. This causes the disc to spin and the mass to fall. How long does it take the mass to fall to the ground? Hint: use torque and angular acceleration. A solid sphere of radius...
A uniform brass solid cylinder has a mass, m = 500 g, and a diameter, D...
A uniform brass solid cylinder has a mass, m = 500 g, and a diameter, D = 6 cm and a length L = 1 m. The cylinder rotates about its axis of rotational symmetry at an angular velocity of 60 radians/s on a frictionless bearing. (a) What is the angular momentum of the cylinder? (b) How much work was required to increase the angular momentum of the cylinder to this value if the cylinder was initially at rest? Once...
Water in pipe AB (Figure 2), diameter (DAB) 1.2 m, is flowing with the velocity (VAB)...
Water in pipe AB (Figure 2), diameter (DAB) 1.2 m, is flowing with the velocity (VAB) of 3 m/second. Then it continues to flow through pipe BC, with a diameter (DBC) of 1.5 m and finally flows through branch pipe of CD, diameter (DCD) of 0.8 m and pipe of CE (DCE), with a velocity (VCE) of 2.1 m/second. Calculate: 1. Discharge of pipe AB (QAB) 2. Flow velocity of pipe BC (VBC) 3. Flow velocity of pipe BC (VBC)...
1a. A car drives around a circular track of diameter 154 m at a constant speed...
1a. A car drives around a circular track of diameter 154 m at a constant speed of 45.1 m/s. During the time it takes the car to travel 97 degrees around, what is the magnitude of the car s average acceleration? b. A car starts from rest, then accelerates at a constant rate over a distance of 63 m. It then immediately decelerates at a constant rate over a distance of 122 m. The entire trip lasts a total duration...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT