Answer :
Final answer:
The weight of the bucket is 117.6 N. As the tension in the rope is 163 N, which is greater than the weight of the bucket, this means the bucket is accelerating upwards. The acceleration of the bucket, calculated using Newton's Second Law, is 3.78 m/s².
Explanation:
To answer this question, we need to understand the concept of tension and how it relates to the weight of an object and its acceleration according to Newton's Second Law. The tension in the rope (T) equals 163 N, and the weight of the bucket (W) equals its mass (12.0 kg) times acceleration due to gravity (9.8 m/s²), so W = (12.0 kg) (9.8 m/s²) = 117.6 N.
Since the tension is greater than the weight, it means the bucket is accelerating upwards. To calculate the acceleration, we subtract the weight from the tension and divide by the mass. This leaves us with a = (T - W) / m = (163 N - 117.6 N) / 12.0 kg = 3.78 m/s² (upwards, hence positive).
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Answer:
The acceleration of the bucket is 3.77m / S ^ 2 up
Explanation:
Hello,
To solve this exercise we must initially draw the free-body diagram (see attached image) of the bucket, and identify the forces present in this case would be the tension force of the rope and the weight of the bucket.
Then use Newton's law that states that the sum of the forces in a body is equal to mass per accession. We will assume that up is positive and down is negative
T=tension=163N
m=mass of bucket =12kg
g=gravity=9.81m/S^2
T-mg=m(a)
[tex]\frac{T-mg}{m} =a\\\frac{163N-(12kg)(9.81m/S^2}{12}=3.77m/s^2[/tex]
The acceleration of the bucket is 3.77m / S ^ 2 up
