Pictured below are two 5.00 gallon Home Depot buckets initially at rest (ignore

Question

Pictured below are two 5.00 gallon Home Depot buckets initially at rest (ignore their masses and assume both buckets hold a full 5.00 gallons). Initially Bucket A has 1.50 liters of water in it and Bucket B is empty. Two hoses are turned on simultaneously and at the following rates: Bucket A is being filled at a rate of 0.250 liters per minute and Bucket B is being filled at 0.450 liters per minute. Will the buckets eventually move? If so, how long (in seconds) after the hoses are turned on do they start to slide?

Explanation / Answer

volume of the bucket=5 gallon=5*3.78541=18.927 ltr

let they slide after t minutes.

have to keep in mind that, to slide:

1. friction force has to be overcome

2. bucket should not be overflowing (ofcourse, once the bucket is fully filled and still it has not moved,

then even if you add more water, amount of water will remain constant)

at time t minutes, amount of water in bucket A=0.25*t ltrs

then mass of bucket A=(0.25*t)*1 kg/ltr=0.25*t kg
weight of bucket A=0.25*t*9.8=2.45*t N

normal force=force along the perpendicular to incline=2.45*t*cos(28)=2.1632*t

then friction force =normal force*static friction coefficient=1.40608*t

tension in the string + component of the weight of bucket A along the incline should balance this friction force so that the bucketds will start sliding

mass of bucket B at time t=0.45*t kg

weight=4.41*t N

then tension in the string=4.41*t N

==>4.41*t+2.45*t*sin(28)=1.40608*t

so as can be seen here, whether the buckets slide does not depend upon time t.

left hand side is greater than right hand side for each time t

hence the blocks will side from the very beginning.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---