A spring balance suspended inside an elevator reads 48\text{ N} when supporting an object … — JAMB UTME

A spring balance suspended inside an elevator reads $48\text{ N}$ when supporting an object while the elevator accelerates downwards at $2\text{ m s}^{-2}$ . Taking acceleration due to gravity $g = 10\text{ m s}^{-2}$ , what is the mass of the object as measured by an equal-arm beam balance?

$6.0\text{ kg}$ Cevap
B
$4.0\text{ kg}$
C
$4.8\text{ kg}$
D
$60.0\text{ kg}$

Cevap

The mass of the object measured by an equal-arm beam balance is

6.0\text{ kg}

In a downward accelerating elevator, the apparent weight indicated by a spring balance is

W_{app} = m(g - a)

. Substituting

48\text{ N} = m(10\text{ m s}^{-2} - 2\text{ m s}^{-2}) = 8m

gives a mass of

6.0\text{ kg}

. Because a beam balance compares masses directly and both sides experience the exact same effective acceleration, it measures true mass regardless of the frame's acceleration.

Adım Adım Çözüm

Formulate the equation for apparent weight in a downward accelerating reference frame.

W_{app} = m(g - a)

When an elevator accelerates downward, the effective acceleration experienced by an object inside is

(g - a)

Substitute the given values (

W_{app} = 48\text{ N}

g = 10\text{ m s}^{-2}

a = 2\text{ m s}^{-2}

) into the formula to find mass

m

48 = m(10 - 2) \implies 48 = 8m \implies m = 6.0\text{ kg}

This yields the true scalar mass of the object.

Determine the reading on an equal-arm beam balance.

The beam balance reads

6.0\text{ kg}

A beam balance compares unknown mass against standard counter-weights; both experience identical effective acceleration, making its measurement independent of motion or local gravity.

Anahtar Kavram

Apparent weight in an accelerating frame vs invariant mass measurement using a beam balance

Tahmini Süre:1m 0s

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