HW Question:Two blocks are connected by a light string that passes over a frictionless pulley, as shown in the figure below. The block of mass m1 = 16.8 kg lies on a horizontal surface and is connected to a spring that has a spring constant k which is really not constant but varies according to the function k=c*x^2 [N/m], where c = 0.231 (constant) with appropriate units. In addition, there is a force of friction acting on m1, such that the coefficient of friction µ is also not constant: μ=bx [unitless], where b is a constant with appropriate units.(a) What are the units of b and c?(b) The system is released from rest when the spring is at its equilibrium length. If the hanging block of mass m2 = 8.45 kg falls a distance h = 1.51 m before it comes to rest, calculate the value of the constant b (don’t forget units).(c) How much work is done by conservative forces? How much work is done by non-conservative forces?(d) What is the net work done by all the forces?Hint: If you need to use integration, you may disregard the units, just assume that all the constants/units work out, but don’t forget the final units that are appropriate for all the variables. Another hint: think about the most convenient location for the reference point. You may have different reference points for the two masses. ### Physics of a Block-Spring System#### Diagram DescriptionThe diagram illustrates a classic physics problem involving a block-spring system with a pulley. 1. **Block and Spring System**: - On a horizontal surface, there is a spring fixed at one end, with a spring constant denoted as \( k \). - Attached to the spring is a block labeled \( m_1 \), indicating its mass. The block is positioned such that it can slide horizontally on a frictionless surface.2. **Pulley System**: - A string is attached to the block \( m_1 \) and runs over a pulley at the edge of the surface. - On the other side of the pulley hangs another block labeled \( m_2 \), also indicating its mass. - The mass \( m_2 \) is depicted as hanging at a vertical distance \( h \) from the ground.#### System Dynamics- **Spring Mechanics**: - The spring can compress or extend, exerting a force on block \( m_1 \) according to Hooke's Law, \( F = -kx \), where \( x \) is the displacement from the equilibrium position.- **Pulley and Gravity**: - The pulley is assumed to be frictionless, allowing the string to move seamlessly. - Block \( m_2 \) experiences a gravitational force equal to \( m_2g \), where \( g \) is the acceleration due to gravity.#### Analysis ObjectivesKey objectives of analyzing this system might include:- Determining the motion of both masses when the system is released from rest.- Calculating the maximum extension or compression of the spring.- Analyzing the energy transformations in the system, such as potential and kinetic energy.This setup is a practical example for exploring fundamental physics concepts such as Newton's laws of motion, energy conservation, and harmonic motion.

Given:- The mass m 1 = 16.8 kg The spring constant k = cx2 where c = 0.231 The mass m2 = 8.45 kg…

Answered: blocks are connected by a light string…

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

Question

HW Question:

Two blocks are connected by a light string that passes over a frictionless pulley, as shown in the figure below. The block of mass m1 = 16.8 kg lies on a horizontal surface and is connected to a spring that has a spring constant k which is really not constant but varies according to the function k=c*x^2 [N/m], where c = 0.231 (constant) with appropriate units. In addition, there is a force of friction acting on m1, such that the coefficient of friction µ is also not constant: μ=bx [unitless], where b is a constant with appropriate units.

(a) What are the units of b and c?

(b) The system is released from rest when the spring is at its equilibrium length. If the hanging block of mass m2 = 8.45 kg falls a distance h = 1.51 m before it comes to rest, calculate the value of the constant b (don’t forget units).

(d) What is the net work done by all the forces?

Hint: If you need to use integration, you may disregard the units, just assume that all the constants/units work out, but don’t forget the final units that are appropriate for all the variables. Another hint: think about the most convenient location for the reference point. You may have different reference points for the two masses.