Determine the velocity of the 60-lb block A if the two...

Name: Determine the velocity of the 60-lb block A if the two blocks are released from rest and the 40-lb block B moves 2 ft up the incline. The coefficient of kinetic friction between both blocks and the inclined planes is ?k = 0.10.
Uploaded: 2022-10-26T12:06:52-08:00
Duration: 6 min 50 s
Channel: Adi S
Description: Determine the velocity of the 60-lb block A if the two blocks are released from rest and the 40-lb block B moves 2 ft up the incline. The coefficient of kinetic friction between both blocks and the inclined planes is ?k = 0.10.

Determine the velocity of the 60-lb block A if the two blocks are released from rest and the 40-lb block B moves 2 ft up the incline. The coefficient of kinetic friction between both blocks and the inclined planes is ?k = 0.10.

Transcript

00:01 Here the free body diagram is as follows.

00:04 So this is the free body diagram.

00:06 This is box a and this represents box b.

00:11 There is angle 60 degree here and here it is 30 degree.

00:16 So there is 40 sign 30 degree and 40 course 30 degree components on block b and 60 sign 60 degree and 60 cost 60 degree components on block a.

00:29 Here we are given mass of block a is equal to 60 pound mass, mass of block b is equal to 40 pound, coefficient of kinetic friction is given which is 0 .1.

00:46 Now from the free body diagram we can say that here normal reaction n a, that is this value is equal to mass of block a into cost, pos -theta.

01:01 Upon substituting the values, here ma is 60 lb into cos, here theta is 60 degree.

01:10 So this turns out to be 30 lb.

01:14 So 30 pound mass is the normal reaction of block a.

01:18 Now the friction force at block a is given by friction force f .a is equal to the coefficient of kinetic friction into the normal reaction of block a.

01:36 So this is equal to 0 .1 into n .a is 30 lb, which we have found out just now upon solving this turns to be 30 pound mass, 30 lb.

01:47 Also, here the normal reaction of block b is equal to mass of block b into cos theta.

01:56 Mass of block b is given which is 40 lb into course here.

02:01 The block b makes an inclination angle of 30 degree.

02:06 Upon solving we will get a normal reaction of block b to be 34 .64 pound mass.

02:13 Now we calculate the friction force at block b.

02:21 The friction force at block b is given by fb is equal to the coefficient of kinetic friction into the normal reaction of block b.

02:31 This is equal to 0 .1 into the normal reaction of block b is 34 .64 pound mass.

02:39 Upon solving we will get 3 .46 pound mass as the friction for set block b...

Question

Determine the velocity of the 60-lb block A if the two blocks are released from rest and the 40-lb block B moves 2 ft up the incline. The coefficient of kinetic friction between both blocks and the inclined planes is ?k = 0.10.

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