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The man and the bucket of bricks

A very good example of Newton's Laws is shown by the following situation.

A bucket of bricks of mass 120 kg is tied to one end of a rope which passes over a frictionless pulley so that it hangs vertically downwards. A man of mass 80 kg hangs onto the other end of the rope.


(See Figure 1).


Calculate:
(a) the tension in the rope holding the man
(b) the tension in the rope holding the bucket
(c) the acceleration of the man
(d) the acceleration of the bucket of bricks
(e) the tensions in the two sections of the rope if it is held stationary on the pulley.

Taking g = 10 ms- 2

Let the tension in the rope be T and the acceleration of the man and bucket of bricks be a.

(a) Consider the forces on the man
T 800 = 80a

Now consider the force on the bucket
1200 T = 120 a

Combining these two equations gives:
a = 2 ms-2 T = 960 N

(b) Since T is the tension throughout the rope the tension in the rope holding the bucket is also 960 N

(c) and (d) a = 2 ms-2

(e) If the rope is held stationary it effectively becomes two sections of rope, with a different tension in each.
800 N (man) 1200 N (bucket and bricks)

 

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© Keith Gibbs 2020