A counterweight of mass $ m = 4.10 \, \text{kg} $ is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius $ R = 7.00 \, \text{cm} $ and mass $ M = 1.80 \, \text{kg} $. The spokes have negligible mass.**Figure Description:**The image depicts a pulley system. A pulley is shown with a hoop and a counterweight $ m $ hanging downwards from a cord wrapped around the pulley. The radius of the pulley is labeled $ R $, and the mass of the pulley hoop is labeled $ M $.**Problems:**(a) What is the net torque on the system about the axle of the pulley?- Enter the magnitude: $\underline{\hspace{2cm}}$ N·m- Direction: [Select](b) When the counterweight has a speed $ v $, the pulley has an angular speed $ \omega = v/R $. Determine the magnitude of the total angular momentum of the system about the axle of the pulley.- $(\underline{\hspace{2cm}} \, \text{kg} \cdot \text{m})v$(c) Using your result from (b) and $\vec{\tau} = \frac{d\vec{L}}{dt}$, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.)- $\underline{\hspace{2cm}}$ m/s²

Given: The mass of the counterweight is m=4.10 kg, The pulley is a thin hoop of radius R=7.00 cm,…

A counterweight of mass m = 4.10 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 7.00 cm and mass M = 1.80 kg. The spokes have negligible mass. (a) What is the net torque on the system about the axle of the pulley? magnitude direction N.m ---Select-- (b) When the counterweight has a speed v, the pulley has an angular speed w = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. kg - m)v (c) Using your result from (b) and ? = dL/dt, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.) |m/s²

A counterweight of mass m = 4.10 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 7.00 cm and mass M = 1.80 kg. The spokes have negligible mass. (a) What is the net torque on the system about the axle of the pulley? magnitude direction N.m ---Select-- (b) When the counterweight has a speed v, the pulley has an angular speed w = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. kg - m)v (c) Using your result from (b) and ? = dL/dt, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.) |m/s²

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)...

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Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

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A counterweight of mass $ m = 4.10 \, \text{kg} $ is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius $ R = 7.00 \, \text{cm} $ and mass $ M = 1.80 \, \text{kg} $. The spokes have negligible mass.

**Figure Description:**
The image depicts a pulley system. A pulley is shown with a hoop and a counterweight $ m $ hanging downwards from a cord wrapped around the pulley. The radius of the pulley is labeled $ R $, and the mass of the pulley hoop is labeled $ M $.

**Problems:**

(a) What is the net torque on the system about the axle of the pulley?
- Enter the magnitude: $\underline{\hspace{2cm}}$ N·m
- Direction: [Select]

(b) When the counterweight has a speed $ v $, the pulley has an angular speed $ \omega = v/R $. Determine the magnitude of the total angular momentum of the system about the axle of the pulley.
- $(\underline{\hspace{2cm}} \, \text{kg} \cdot \text{m})v$

(c) Using your result from (b) and $\vec{\tau} = \frac{d\vec{L}}{dt}$, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.)
- $\underline{\hspace{2cm}}$ m/s²

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