a) What is the acceleration of the hanging mass? (Indicate the direction with th

Question

a) What is the acceleration of the hanging mass? (Indicate the direction with the sign of your answer.)
m/s2

(b) Determine the tension in the cord. (Indicate the direction with the sign of your answer.)
N

A block of mass m1 = 34 kg on a horizontal surface is connected to a mass m2 = 17.4 kg that hangs vertically as shown in the figure below. The two blocks are connected by a string of negligible mass passing over a frictionless pulley. The coefficient of kinetic friction between m1and the horizontal surface is 0.28. (Assume gravity acts toward the +y direction and the +x-axis is parallel to the surface and to the right.)

Explanation / Answer

assuming the system to move downwards the acceleration for body 1 will be in the positive X direction and the acceleration for body 2 will be downwards +Y direction.

equation for mass 1.

friciton force opposing relative motion will be opposite to the direction of acceleration. hence friction force will act in -X direction

let co effectient of friciton be ?,

hence F = ?.N where N = m1g.

now equation of motion for m1

T - F = m1a

T = ( ?.m1.g + m1a) = ( 0.28*34*9.81 + 34 a) = ( 93.3912 + 34 a ) ........... (A)

equation of motion for body 2

T - m2g = m2a

T = ( 17.4 * 9.81 + 17.4 a ) = (170.694 + 17.4 a ) .............................................(B)

equating (A) and (B)

16.6a = 77.1288

answer (a) acceleration = 4.646 m/s2

using equation (B) to find Tension = T

answer (b) T = 17.4 ( 4.646 + 9.81 ) = 251.5344 N.

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