[table]
Which of the following scenarios represents objects in static equilibrium? i. A folder resting on a shelf. ii. A coin at its highest point after being tossed into the air. iii. A person spinning on a carousel with a constant angular velocity. iv. A lorry speeding up on an expressway.
[/table]

Question

BlackTom AI · Accepted Answer

Question restatement: Which of the following scenarios represents objects in static equilibrium? i. A folder resting on a shelf. ii. A coin at its highest point after being tossed into the air. iii. A person spinning on a carousel with a constant angular velocity. iv. A lorry speeding up on an expressway.

Option a: a. [table]
(i) only
[/table]
- This option claims that only scenario (i) satisfies static equilibrium. In analyzing static equilibrium, we look for two main conditions: (1) the net force on the object is zero (translational equilibrium) and (2) the net torque about any point is zero (rotational equilibrium). For (i) A folder resting on a shelf, the weight is balanced by the normal contact force from the shelf, producing zero net force, and there is no tendency to rotate because the contact forces pass through or balance the line of action in a way that yields zero net torque about the folder’s center of mass. This makes (i) a candidate for static equilibrium.

Option b: b. [table]
(ii) and (iv) only
[/table]
- This asserts that both (ii) and (iv) are in static equilibrium. Scenario (ii) places the coin at its highest point in a vertical toss, where the instantaneous velocity is zero but the acceleration is downward due to gravity. Even though the velocity is momentarily zero, there is a nonzero net force (gravity) acting on the coin, so translational equilibrium is not satisfied. For (iv) a lorry speeding up, there is a net forward force causing acceleration, so both translational and rotational equilibrium are not satisfied. Therefore, this option fails to correctly identify static equilibrium candidates.

Option c: c. [table]
None of the above
[/table]
- Declaring none of the scenarios as static equilibrium would require that every listed scenario violates at least one equilibrium condition. As discussed, (i) meets the criteria for static equilibrium in a simple contact situation, making this option inconsistent with the observation that at least one scenario (i) does satisfy equilibrium.

Option d: d. [table]
(i), (ii) and (iii) only
[/table]
- This choice groups three scenarios as satisfying static equilibrium. We have already reasoned that (ii) is not in equilibrium due to gravitational acceleration despite zero velocity, and (iii) involves continuous rotation with centripetal acceleration and, in general, a nonzero net torque for maintaining that motion, so it is not in static equilibrium. Therefore, this option incorrectly includes (ii) and (iii).

Option e: e. [table]
(i) and (iii) only
[/table]
- This suggests that both (i) and (iii) satisfy static equilibrium. As noted, (iii) involves rotational motion with constant angular velocity, which requires a centripetal force and typically a nonzero internal torque balance to maintain rotation; the presence of rotational motion means the system is not in static equilibrium in the translational sense, even if angular velocity is constant. Thus this option mislabels (iii) as equilibrium.

Summary of reasoning across options: The core test is whether the net force and net torque vanish. Scenario (i) features a stationary object with normal and gravitational forces balanced and no rotation tendency, aligning with static equilibrium. Scenarios (ii), (iii), and (iv) each fail one or both equilibrium conditions: (ii) has gravity acting while velocity is zero, but acceleration is nonzero; (iii) involves rotation with centripetal forces and potential torques that prevent static translational equilibrium; (iv) involves acceleration due to a net forward force, breaking translational equilibrium. The comparison shows only (i) satisfies the required conditions while the others do not, though this conclusion is presented through examining each case’s forces and motions rather than a summary label.

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