**Problem Description:**A block of mass \( m_1 = 1.90 \, \text{kg} \) and a block of mass \( m_2 = 6.35 \, \text{kg} \) are connected by a massless string over a pulley in the shape of a solid disk with radius \( R = 0.250 \, \text{m} \) and mass \( M = 10.0 \, \text{kg} \). The fixed, wedge-shaped ramp makes an angle of \( \theta = 30.0^\circ \) as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks.**Tasks:**(a) Draw force diagrams of both blocks and of the pulley.- [Option to upload file](b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.)- Answer box available for response in \( \text{m/s}^2 \).(c) Determine the tensions in the string on both sides of the pulley.- Answer box for the tension on the left of the pulley in Newtons (N).- Answer box for the tension on the right of the pulley in Newtons (N).**Diagram Explanation:**The diagram shows a block \( m_1 \) resting on a flat surface, connected by a string to a block \( m_2 \) that is on a ramp inclined at \( \theta = 30.0^\circ \). The string passes over a pulley that is represented as a solid disk. The forces acting on the blocks include gravitational force, normal force from the surfaces, tension from the string, and frictional force opposing motion.The problem involves understanding the dynamics of this system, considering forces, tensions, and friction.

Force diagram of m1 block; Force diagram of m2 block; Force diagram of pulley Equation of motion of mass m1: m1a=T1-Ff1Ff1=μkN1Ff1=μkm1ghence,m1a=T1-μkm1g 1) Equation of motion of mass m2: m2a=m2gsinθ-T2-Ff2Ff2=μkm2gcosθm2a=m2gsinθ-T2-μkm2gcosθ 2) Net torque exerts on pulley; Iα=T2R-T1R12MR2aR=T2R-T1R12Ma=T2-T1 3) Now, adding equation-1), 2) and 3): m1+m2+12Ma=m2gsinθ-μkgm1+m2cosθ 4) Values given in the question are as follow; m1=1.9 kgm2=6.35 kgR=0.250 mM=10 kgθ=30°μk=0.360 g=9.8ms2 Substitute known values in equation-4); 1.9+6.35+1210a=6.35×9.8×sin30-0.360×9.81.9+6.35cos30a=31.115-26.10413.25a=0.38 ms2 Tension in a string on m1 side: Substitute known values in equation-1): 1.9×0.38=T1-0.36×1.9×9.8T1=0.722+6.703T1=7.42 N Tension in a string on m1 side: Substitute known values in equation-2): 6.35×0.38=6.35×9.8×sin30-T2-0.36×6.35×9.8×cos30T2=31.115-2.413-19.401T2=9.301 N

Science

Physics

A block of mass m, = 1.90 kg and a block of mass m, = 6.35 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of 0 = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. М, R (a) Draw force diagrams of both blocks and of the pulley. Choose File No file chosen This answer has not been graded yet. (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s² (c) Determine the tensions in the string on both sides of the pulley. left of the pulley right of the pulley N

A block of mass m, = 1.90 kg and a block of mass m, = 6.35 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of 0 = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. М, R (a) Draw force diagrams of both blocks and of the pulley. Choose File No file chosen This answer has not been graded yet. (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s² (c) Determine the tensions in the string on both sides of the pulley. left of the pulley right of the pulley N

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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