[OCR] 2

Topic: Atomic Structure

A uniform square box with sides 0.80 m and mass 2.0 kg is at rest on the ground. One end of a light rope is attached to the box and the other end is attached to the wheel of a motor. The motor applies a constant clockwise torque of 5.0 N m on the wheel of radius 0.20 m .\n\nAt the instant shown in Fig. 2.1, the rope is taut and it makes an angle of $\theta=20^{\circ}$ with the vertical side of the box. The system remains in equilibrium.\n\nFig. 2.1 [8.0m]

Part 1: (a) Calculate the tension in the rope.\n$$\text { tension }=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$$\n$$ [2m]

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Part 2: (b) Point $M$ is the mid-point at the base of the box as shown in Fig. 2.1.\n\nBy taking moments about point $M$, determine the horizontal distance $d$ between $M$ and the point at which the contact force by the ground acts on the box. [3m]

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Part 3: (c) The motor is shifted to the right such that $\theta$ increases. The torque applied by the motor remains constant.\n\nWithout any further calculations, explain why there is a maximum value of $\theta$ for which equilibrium can be maintained. [3m]

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