A frictionless surface is inclined at an angle of = 35.7° to the horizontal. A 2

Question

A frictionless surface is inclined at an angle of = 35.7° to the horizontal. A 270-g block on the ramp is attached to a 75.0-g block using a pulley, as shown in the figure below. (a) Draw two free-body diagrams, one for the 270-g block and the other for the 75.0-g block. (Do this on paper. Your instructor may ask you to turn in your work.) (b) Find the tension in the string and the magnitude of the acceleration of the 270-g block. N m/s2 (c) The 270-g block is released from rest. How long does it take for it to slide a distance of 1.20 m along the surface? s (d) Will it slide up the incline, or down the incline? slide down the incline slide up the incline

Explanation / Answer

given,

angle = 35.7 degree

mass of block 1 = 270 gm

mass of block 2 = 75 gm

force equation of block 2

T - m2g = m2a

T - 0.075 * 9.8 = 0.075a

force equation of block 1

m1g*sin(35.7) - T = m1a

0.27 * 9.8 * sin(35.7) - T = 0.27a

on solving we'll get

tension T = 0.91088 N

acceleration a = 2.34507 m/s^2

s = ut + 0.5 * at^2

1.2 = 0 + 0.5 * 2.34507 * t^2

time it'll take to slide 1.2 m = 1.011 sec

it'll slide down as mg * sin(theta) is greater than tension

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