/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 52 An object is suspended from a sp... [FREE SOLUTION] | 91Ó°ÊÓ

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An object is suspended from a spring balance in a lift. The reading is \(240 \mathrm{~N}\) when the lift is at rest. If the spring balance reading now changes to \(220 \mathrm{~N}\), then the lift is moving a. downward with constant speed b. downward with decreasing speed c. downward with increasing speed d. upward with increasing speed

Short Answer

Expert verified
c. downward with increasing speed

Step by step solution

01

Understand the weight measurements

The weight of the object when the lift is at rest is 240 N. This means that gravity's force acting on the object is 240 N, which can be calculated as \(mg = 240\, \text{N}\), where \(m\) is the mass and \(g\) is the acceleration due to gravity.
02

Analyze the new reading

The new reading on the spring balance is 220 N. This decrease indicates a change in the effective gravitational force experienced by the object.
03

Apply the concept of apparent weight

When the lift is in motion, the apparent weight of the object changes. If the lift accelerates downwards, the apparent weight decreases, which explains the lower reading of 220 N on the spring balance.
04

Determine the direction and type of acceleration

A decreasing reading from 240 N to 220 N suggests that the lift is accelerating downward, because this would make the net force less than the gravitational force acting alone. Hence, the lift is moving downward with increasing speed.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Apparent Weight
When you think of weight, you might imagine the consistent force gravity exerts upon an object. However, when an object is in motion, especially in a moving lift, what you perceive as weight is actually called "apparent weight." Apparent weight is the force exerted by an object on a surface, like a weighing scale or a spring balance, due to both gravity and any additional acceleration. In a lift, when the apparent weight is different from the actual gravitational weight, it reflects the effect of acceleration. The lift's motion redistributes how forces act on the object. If a lift accelerates upward, the apparent weight seems heavier. Conversely, if the lift accelerates downward, it feels lighter. In our scenario, since the apparent weight dropped from 240 N to 220 N, it indicates a decrease in force, most likely due to downward acceleration.
Accelerated Motion
Accelerated motion refers to any change in the velocity of an object due to a force being applied. In our case with the lift, acceleration comes into play as the lift's velocity changes. This can happen if the lift starts moving after being at rest, speeds up, or slows down. When the lift is accelerating in a particular direction, its motion affects the reading on a scale due to Newton's Laws of Motion. Specifically, Newton's second law states that an object will accelerate in the direction of a net applied force:
  • If a lift accelerates upward, the object feels heavier, resulting in a higher reading on the spring balance.
  • If a lift accelerates downward, the reading decreases because the object feels lighter.
Understanding accelerated motion explains why the spring balance in the lift showed a decrease in apparent weight from 240 N to 220 N, indicating the lift was moving downward and speeding up.
Spring Balance Reading in a Lift
A spring balance provides a visual and measurable way to see changes in forces acting on an object in a lift. The balance measures the force exerted by the object, which varies when the lift moves due to changes in acceleration. In a stationary lift, the spring balance shows the actual gravitational force (the true weight of the object). However, when the lift starts to accelerate, the spring balance reading either increases or decreases depending on the lift's direction:
  • If the lift accelerates upwards, it causes an increased tension in the spring, showing a heavier reading.
  • If the lift accelerates downwards, like in our exercise, the tension decreases, showing a lighter reading, which matches the 220 N reading observed when the lift was accelerating downward.
This change in the reading is an excellent illustration of how forces work in tandem with motion, and observing it helps predict the motion and acceleration direction of the lift.

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