### Description of the Disk and Block SystemA uniform horizontal disk with a radius of 5.50 m rotates without friction at an angular velocity of \( \omega = 2.30 \) revolutions per second. The disk has a feedback mechanism that senses its angular speed. A drive motor at point A maintains the system's constant angular speed. A block with a mass of \( m = 1.20 \) kg sits on the disk's center and slides outward in a radial slot. Starting at \( t = 0 \), the block moves at a constant speed \( v = 1.25 \) cm/s relative to the disk until reaching the edge at \( t = 465 \) s. There's no friction during this sliding, and the block's motion is further constrained by a brake at B, which induces tension in a string tied to the block.#### Key Tasks and Calculations- **(a) Calculating Torque:** Determine the function of time that describes the torque the drive motor provides while the block is sliding. The formula to use is \( \tau = 2mr\omega v \).- **(b) Torque at a Specific Time:** Calculate the torque at \( t = 465 \) s, right before the block finishes sliding. - **Answer:** 2.52 N·m- **(c) Calculating Power:** Find the function for power delivered by the drive motor over time.- **(d) Power at the End of the Slot:** Identify the power when the block reaches the end of the slot. - **Answer:** 18.2 W (incorrect in the original transcript)- **(e) String Tension:** Compute the string tension as a function of time.- **(f) Motor Work Done:** Calculate the work done by the drive motor during the 465 s motion. The formula given is \( W_{\text{motor}} = mv^2\omega^2t^2 \). - **Answer:** 8.47 kJ- **(g) Work Done by String Brake:** Find the work done by the string brake on the sliding block, which is negative due to the opposing direction. - **Formula:** \( W_{\text{block}} = -\frac{1}{2}mv^2\omega^2t^2 \). - **Answer:** -4.23 kJ- **(h

Answered: Image /qna-images/answer/f6b20c80-1daf-4aad-a8ec-643596afecd7.jpgThe sliding block reaches the end of the block at 465 sPower = 0.0783tPower = 0.0783(465)Power = 36.41 W

Science

Physics

A uniform horizontal disk of radius 5.50 m turns without friction at = 2.30 rev/s on a vertical axis through its center, as in the figure below. A feedback mechanism senses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant while a m = 1.20 kg block on top of the disk slides outward in a radial slot. The block starts at the center of the disk at time t = 0 and moves outward with constant speed v = 1.25 cm/s relative to the disk until it reaches the edge at t = 465 s. The sliding block experiences no friction. Its motion is constrained to have constant radial speed by a brake at B, producing tension in a light string tied to the block. (a) Find the torque as a function of time that the drive motor must provide while the block is sliding. Hint: The torque is given by T 2mrvw. = t N.m (b) Find the value of this torque at t = 465 s, just before the sliding block finishes its motion. 2.52 N-m (c) Find the power which the drive motor must deliver as a function of time. t W/s (d) Find the value of the power when the sliding block is just reaching the end of the slot. 18.2 x w (e) Find the string tension as a function of time. ]t N/s

A uniform horizontal disk of radius 5.50 m turns without friction at = 2.30 rev/s on a vertical axis through its center, as in the figure below. A feedback mechanism senses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant while a m = 1.20 kg block on top of the disk slides outward in a radial slot. The block starts at the center of the disk at time t = 0 and moves outward with constant speed v = 1.25 cm/s relative to the disk until it reaches the edge at t = 465 s. The sliding block experiences no friction. Its motion is constrained to have constant radial speed by a brake at B, producing tension in a light string tied to the block. (a) Find the torque as a function of time that the drive motor must provide while the block is sliding. Hint: The torque is given by T 2mrvw. = t N.m (b) Find the value of this torque at t = 465 s, just before the sliding block finishes its motion. 2.52 N-m (c) Find the power which the drive motor must deliver as a function of time. t W/s (d) Find the value of the power when the sliding block is just reaching the end of the slot. 18.2 x w (e) Find the string tension as a function of time. ]t N/s

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: what is the angular speed when she is 0.554 m from the center?

A: Conservation of Angular Momentum If the net external torque acting on a rigid body or a particle is…

Q: The tub of a washer goes into its spin-dry cycle, starting from rest and reaching an angular speed…

A: Given: Angular speed of the tub is 5.0 rev/s. Time taken to reach the angular speed of 5.0 rev/s is…

Q: A solid disk of mass 1.20 kg and radius 20.0 cm is rotating at 1500 revolutions per minute (rpm)…

A: mass of the solid disc = 1.2 kg radius of the disc R= 0.2mangular velocity…

Q: A box slides down a ramp, Resting on a table. When it reaches the bottom of the tamp, the box leaves…

A: Please see the next step for solution:-

Q: A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a…

A: Given Information:- Radius of the horizontal platform is R=3.56 m Moment of inertia of the circular…

Q: A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a…

Q: In the figure, a solid 0.4 kg ball rolls smoothly from rest (starting at height H-6.1 m) until it…

Q: Jennifer decided to install a ceiling fan in the master bedroom. After a laborious installation, she…

A: initial angular speed (w) = 0 final angular speed = 120 rev/min = 2 rev/sec = 12.57 rad/s t = 20…

Q: A wheel is rotating about an axis that is in the Z-direction. The angular velocity ωzωz is -6.00…

A: Initial time, ti = 0 sec Initial angular velocity, ωi = (-) 6 rad/sec After some time, tf = 14 sec…

Q: A particle rotates about a fixed axis in an orbit of radius 20 cm with an angular acceleration of…

A: ACCORDING TO QUETION GIVEN IS RADIUS IS = 20 CM = .2 M ANGULAR ACCELERATION = 4 rad/sec…

Q: A solid disk of mass M = 0.600 kg and radius R = 0.250 m is suspended vertically and is free to…

Q: horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a…

Q: Mary is an avid game show fan and one of the contestants on a popular game show. She spins the…

A: The angle through which the wheel spin in 5.5 revolutions is, Δθ=5.52π rad=11π rad The equation of…

Q: An annular cylinder (mass 3.4 kg) with inner radius R1 = 15 cm and outer radius R2 = 39 cm is…

Q: particular horizontal turntable can be modeled as a uniform disk with a mass of 230 g and i gular…

Q: One method of pitching a softball is called the "windmill" delivery method, in which the pitcher's…

Q: In a softball windmill pitch, the pitcher rotates her arm through just over half a circle, bringing…

A: Given data *The initial angular velocity is ωi = 12.0 rad/s *The final angular velocity is ωf = 24.0…

Q: A discus thrower with an arm length of 1.20 meters starts from rest and begins to rotate…

A: Arm length r = 1.2 m.Angular accelaeration

Q: In the figure, a cockroach with mass m rides on a disk of mass 2.8m and radius R. The disk rotates…

A: Given: mass of cockroach- m mass of disk - 2.8m radius of disc- R angular speed, ωi = 0.8 rad/s…

Q: A playground ride consists of a disk of mass M = 38 kg and radius R = 1.5 m mounted on a…

Q: Starting at the point (4.57 m,0 m) on the x–y plane, a physics student runs around the origin…

A: Given value--- starting point = (4.57m , 0m ) speed = 2.09 m/s . time = 11.1 s. We have to find---…

Q: A particle rotates about a fixed axis in an orbit of radius 20 cm with an angular acceleration of…

Q: Some power stations and vehicles use spinning disks to store energy (known as flywheel energy…

A: Given that:m=900 kgr=0.45 mα=-1.3 rad/s2θ=5.6×105 rad

Q: A 40.0-cm diameter disk rotates with a constant angular acceleration of 2.60 rad/s2. It starts from…

Q: A carousel (counter-clockwise merry-go-round) starts from rest and accelerates at a constant angular…

A: Given angular acceleration = 0.02 rev/s2 iinitial angular speed = 0 radius of rotation for girl =…

Q: A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a…

Q: A uniform horizontal disk of radius 5.50 m turns without friction at = 2.30 rev/s on a vertical axis…

Q: A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a…

A: Solution: Given: r1 = radius of merry go round = 1.54 m I1 = rotational inertia of merry go round =…

Q: A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a…

A: Mass of the student (m) = 73.1 kg Radius of the platform(R) = 1.83 m Rotational inertia of disk =…

Q: A student gives a steady push to a ball at the end of a massless, rigid rod for 1 s, causing the…

Q: A small fan has blades that have a radius of 0.0600 m. When the fan is turned on, the tips of the…

Q: During the spin cycle the time dependent angular speed of a washing machine drum is given by the…

Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

### Description of the Disk and Block System

A uniform horizontal disk with a radius of 5.50 m rotates without friction at an angular velocity of \( \omega = 2.30 \) revolutions per second. The disk has a feedback mechanism that senses its angular speed. A drive motor at point A maintains the system's constant angular speed. A block with a mass of \( m = 1.20 \) kg sits on the disk's center and slides outward in a radial slot. Starting at \( t = 0 \), the block moves at a constant speed \( v = 1.25 \) cm/s relative to the disk until reaching the edge at \( t = 465 \) s. There's no friction during this sliding, and the block's motion is further constrained by a brake at B, which induces tension in a string tied to the block.

#### Key Tasks and Calculations

- **(a) Calculating Torque:** Determine the function of time that describes the torque the drive motor provides while the block is sliding. The formula to use is \( \tau = 2mr\omega v \).

- **(b) Torque at a Specific Time:** Calculate the torque at \( t = 465 \) s, right before the block finishes sliding.
- **Answer:** 2.52 N·m

- **(c) Calculating Power:** Find the function for power delivered by the drive motor over time.

- **(d) Power at the End of the Slot:** Identify the power when the block reaches the end of the slot.
- **Answer:** 18.2 W (incorrect in the original transcript)

- **(e) String Tension:** Compute the string tension as a function of time.

- **(f) Motor Work Done:** Calculate the work done by the drive motor during the 465 s motion. The formula given is \( W_{\text{motor}} = mv^2\omega^2t^2 \).
- **Answer:** 8.47 kJ

- **(g) Work Done by String Brake:** Find the work done by the string brake on the sliding block, which is negative due to the opposing direction.
- **Formula:** \( W_{\text{block}} = -\frac{1}{2}mv^2\omega^2t^2 \).
- **Answer:** -4.23 kJ

- **(h

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Information given in the question

VIEW

Step 2: Part a - Torque as a function of time

VIEW

Step 3: Part b - Value of torque at 465s

VIEW

Step 4: Part c - Power as a function of time

VIEW

Step 5: Part d- Value of power

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Angular speed, acceleration and displacement

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Starting from rest at t = 0, a wheel undergoes a constant acceleration from t = 0 to t = 10 s. When t = 3.0 s, the angular velocity of the wheel is 6.0 rad/s. Through what angle does the wheel rotate from t = 0 to t = 20 s.
A ball of radius 0.200 m rolls with a constant linear speed of 2.65 m/s along a horizontal table. The ball rolls off the edge and falls a vertical distance of 2.30 m before hitting the floor. What is the angular displacement of the ball while the ball is in the air?
A playground ride consists of a disk of mass M = 38 kg and radius R = 1.5 m mounted on a low-friction axle (see figure below). A child of mass m = 24 kg runs at speed v = 2.5 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. R m M
A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a radius of 2.36 m and a rotational inertia of 218 kg-m2 about the axis of rotation. A 72.6 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 2.07 rad/s when the student starts at the rim, what is the angular speed when she is 0.433 m from the center? Number i Units
A turntable 46.0 cm in diameter diameter starts from rest, and rotates at 68.0 rpm at its first complete revolution with constant angular acceleration. If it maintains the same acceleration, a) what is the rotational speed at time 34.0 seconds? b) what is the tangential speed of a point 10 cm from the edge of the turntable at time 34.0 seconds?
A wheel rotating with a constant angular acceleration turns through 15 revolutions during a 2 s time interval. Its angular velocity at the end of this interval is 18 rad/s. What is the angular acceleration of the wheel? Note that the initial angular velocity is not zero. Your answer
Your grandmother enjoys creating pottery as a hobby. She uses a potter's wheel, which is a stone disk of radius R = 0.540 m and mass M = 100 kg. In operation, the wheel rotates at 45.0 rev/min. While the wheel is spinning, your grandmother works clay at the center of the wheel with her hands into a pot-shaped object with circular symmetry. When the correct shape is reached, she wants to stop the wheel in as short a time interval as possible, so that the shape of the pot is not further distorted by the rotation. She pushes continuously with a wet rag as hard as she can radially inward on the edge of the wheel and the wheel stops in 6.00 s. You would like to build a brake to stop the wheel in a shorter time interval, but you must determine the coefficient of friction (?k) between the rag and the wheel in order to design a better system. You determine that the maximum pressing force your grandmother can sustain for 6.00 s is 65.0 N. What If? If your grandmother instead chooses to press…
At t= 0 a grinding wheel has an angular velocity of 30.0 rad/s. It has a constant angular acceleration of 35.0 rad/s² until a circuit breaker trips at time t = 1.70 s. From then on, it turns through an angle 438 rad as it coasts to a stop at constant angular acceleration. Through what total angle did the wheel turn between t= 0 and the time it stopped? Express your answer in radians. 8= Submit Part B - ΑΣΦΑ 1 V Part C Request Answer At what time did it stop? Express your answer in seconds. Submit ΓΨΓ ΑΣΦ 3 Request Answer 2 @ 3 C www. 7 ΑΣΦ) → O ? What was its acceleration as it slowed down? Express your answer in radians per second squared. ? ? rad S Review Const
In a popular amusement park ride, a rotating cylinder of radius R = 2.00 m is set in rotation at an angular speed of 6.10 rad/s, as in the figure shown below. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider's clothing and the wall is needed to keep the rider from slipping?
Starting from rest, a wheel undergoes a constant acceleration for 10 seconds. When t = 3.0 s, the angular velocity of the wheel is 6.0 rad/s. Find the total angle the wheel rotates from t = 0 to t = 20 s.
A student gives a steady push to a ball at the end of a massless, rigid rod for 1 s, causing the ball to rotate clockwise in a horizontal circle as shown below. The rod’s pivot is frictionless. Sketch a graph of the ball’s angular velocity as a function of time for the first 3 s of the ball’s motion. You won’t be able to include numbers on the vertical axis, but your graph should have the correct sign and the correct shape
A Texas cockroach walks from the center of a circular disk (that rotates like a merry-go-round without external torques) out to the edge at radius R. The angular speed of the cockroach–disk system for the walk is (va = 5.0 rad/s and vb = 6.0 rad/s). After reaching R, what fraction of the rotational inertia of the disk does the cockroach have?