Two blocks are positioned on surface, each inclined at the same angle26.8 degree
ID: 1490501 • Letter: T
Question
Two blocks are positioned on surface, each inclined at the same angle26.8 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 4.8 kg, and the coefficient of friction for both blocks and inclines is ? =0.04 Assume gravity is g=10 m/s^2
a) what must be the mass of the white block if both blocks are slide to the right at constant velocity? (answer in Kg)
b) what must be the mass of the white block if both blocks are to slide to the left at constant velocity? (Answer in Kg)
c) What must be the mass of the white block if both blocks are to slide to the right at an acceleration of 1.5 m/s^2? ( answer in Kg)
d) What must be the mass of the white block if both blocks are t slide to the left at an acceleration of 1.5 m/s^2? (Answer in Kg)
Explanation / Answer
(a) Since both the blocks will move with constant velocity, so the net force must be zero. Now since these are inclined at equal angles from the horizontal and the friction coefficient is same for them, so the friction force acting on them will be equal and cancel out each other. Now the only force acting on them will be component of gravity, which should be equal. Sine the inclination angle is equal so the mass must also be equal. Hence the mass of other block will also be 4.8 Kg.
(b)Since in this question also net force will be zero and it does not depend on the direction of the motion. By similar logic as explained in question 1 the mass of the blocks should be same. So mass of other block should be 4.8 Kg.
(c)In this system acceleration is given by
a=(m1-m2)g*sin(theta)/(m1+m2)
1.5=(4.8-m2)*9.8*0.45/(4.8+m2)
1.632+0.34m2=4.8-m2
1.34m2=3.167
m2=2.36 Kg
(d)Similarly
1.5=(m2-4.8)*9.8*0.45/(4.8+m2)
1.632+0.34m2=m2-4.8
0.66m2=6.432
m2=6.432/.66
m2=9.745 Kg
(e)Since even if there was friction the effect of friction on both blocks was same and hence it was canceled out by each other. So if friction is not there then also the scenario will not change.
Hence the answers to all parts will be same even if the surface is frictionless.
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