Question

Mario is doing pull-ups about 1 meter from the end of the hour hand of a clock on the Big Ben Tower in London.

Mario weighs 650N and the Hour hand weighs 5000N and is uniform in density. The time is 3pm. The Hour hand is 5 meters long. What is the net Torque around the pin that attaches the hour hand to the clock face?

Answer 1

Answer on Question #53229 - Physics - Mechanics - Kinematics - Dynamics

Mario is doing pull-ups about $l = 1$ meter from the end of the hour hand of a clock on the Big Ben Tower in London. Mario weighs $W_{M} = 650\mathrm{N}$ and the Hour hand weighs $W = 5000\mathrm{N}$ and is uniform in density. The time is $3\mathrm{pm}$ . The Hour hand is $L = 5$ meters long. What is the net Torque around the pin that attaches the hour hand to the clock face?

Solution:

The forces which act on the Hour hand are shown in the figure above. Since the pull-ups is the periodic process the net force acting on the Hour hand due to Mario's weight is $W_{M}$ . Therefore the net torque around the pin is given by

$$\tau = \frac {L}{2} W + W _ {M} (L - l) = \frac {5 \mathrm {m}}{2} 5 0 0 0 \mathrm {N} + 6 5 0 \mathrm {N} (5 \mathrm {m} - 1 \mathrm {m}) = 1 5. 1 \mathrm {k N} \cdot \mathrm {m}$$

Answer: $15.1\mathrm{kN}\cdot \mathrm{m}$

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