**Problem (c): Calculation of Gravitational Torque in a Pendulum**A small ball of mass 0.75 kg is attached to one end of a 1.25 m long massless rod, and the other end of the rod is hung from a pivot. When the resulting pendulum is 30° from the vertical, what is the magnitude of the gravitational torque calculated about the pivot?To calculate the gravitational torque (\(\tau\)) about the pivot, we can use the formula:\[ \tau = r \cdot F \cdot \sin(\theta) \]where:- \( r \) is the length of the rod (1.25 m)- \( F \) is the force due to gravity acting on the mass (mg), where \( m \) is the mass (0.75 kg) and \( g \) is the acceleration due to gravity (approximately 9.8 m/s²)- \(\theta\) is the angle from the vertical (30°)First, calculate the force \( F \):\[ F = m \cdot g \]\[ F = 0.75 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \]\[ F = 7.35 \, \text{N} \]Next, calculate the torque:\[ \tau = 1.25 \, \text{m} \cdot 7.35 \, \text{N} \cdot \sin(30°) \]\[ \sin(30°) = 0.5 \]\[ \tau = 1.25 \, \text{m} \cdot 7.35 \, \text{N} \cdot 0.5 \]\[ \tau = 4.59375 \, \text{Nm} \]Therefore, the magnitude of the gravitational torque about the pivot is approximately **4.59 Nm**.

given that,l=1.25 mθ=30°m=0.75 kgg=9.8 ms2

(c) A small ball of mass 0.75 kg is attached to one end of a 1.25 m long massless rod, and the other end of the rod is hung from a pivot. When the resulting pendulum is 30° from the vertical, what is the magnitude of the gravitational torque calculated about the pivot?

(c) A small ball of mass 0.75 kg is attached to one end of a 1.25 m long massless rod, and the other end of the rod is hung from a pivot. When the resulting pendulum is 30° from the vertical, what is the magnitude of the gravitational torque calculated about the pivot?

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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