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al
updated 1 month ago

One 3.2-kg paint bucket is hanging by a massless cord from another 3.2-kg paint bucket, also hanging by a mass-less cord

One 3.2-kg paint bucket is hanging by a massless cord from another 3.2-kg paint bucket, also hanging by a mass-less cord, as shown in Fig. 4–49. (a) If the buckets are at rest, what is the tension in each cord? (b) If the two buckets are pulled upward with an acceleration of 1.25 m/s2 by the upper cord, calculate the tension in each cord. You need to draw a FBD for each bucket.

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1 Answer
ba
updated 11 months ago

Here , mass of bucket ,m = 3.2 Kg

Now , let the tension in upper rope is T1

the tension in the middle rope is T2

a)

For lower bucket, balancing forces in vertical direction

T2 - mg = 0

T2 = mg

T2 = 3.2 *9.8

T2 = 31.36 N

tension in the middle rope is 31.36 N

For the upper bucket , balancing forces in vertical direction

T1 - T2 - mg = 0

T1 = T2 + 3.2 *9.8

T1 = 62.72 N

the tension in the upper rope is 62.72 N

B)

for a = 1.25 m/s^2

Using second law of motion ,for both the buckets

Fnet = ma

T1 - 2mg = 2m*a

T1 = 2*3.2*(9.8 +1.25)

T1 = 70.72 N

the tension in the upper rope is 70.7 N

Now , the lower bucket

Using second law of motion,

T2 - mg = ma

T2 = 3.2 * (9.8 + 1.25)

T2 = 35.36 N

the tension in the lower rope is 35.36 N

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