Question

a weight of 442N sits on a table connected by a massless string to a 185N block that is dangling above the ground with the string draped over a pulley. ignoring all frictional effects and assuming the pulley to be massless, find the acceleration and the tension in the rope.

Answer 1

Answer on Question #57059, Physics / Other

A weight of 442N sits on a table connected by a massless string to a 185N block that is dangling above the ground with the string draped over a pulley. Ignoring all frictional effects and assuming the pulley to be massless, find the acceleration and the tension in the rope.

Solution:

Given:

$$W _ {1} = 4 4 2 \mathrm {N}$$ $$W _ {2} = 1 8 5 \mathrm {N}$$ $$a = ?$$ $$T = ?$$

The masses of blocks are

$$m _ {1} = \frac {W _ {1}}{g} = \frac {4 4 2}{9 . 8 1} = 4 5. 0 6 \mathrm {k g}$$ $$m _ {2} = \frac {W _ {2}}{g} = \frac {1 8 5}{9 . 8 1} = 1 8. 8 6$$

The equations of motion are:

$$m _ {1} a = T$$ $$m _ {2} a = W _ {2} - T$$

The adding of two equations gives:

$$m _ {1} a + m _ {2} a = W _ {2}$$

Thus, the acceleration is

$$a = \frac {W _ {2}}{m _ {1} + m _ {2}} = \frac {1 8 5}{4 5 . 0 6 + 1 8 . 8 6} = 2. 8 9 \mathrm {m / s ^ {2}}$$

The tension from first equation is

$$T = m _ {1} a = 4 5. 0 6 \cdot 2. 8 9 = 1 3 0. 2 \mathrm {N}$$

Answer: $a = 2.89 \, \text{m/s}^2$ ; $T = 130.2 \, \text{N}$

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