A rocket carries a payload of mass 25\text{ kg} resting on a spring balance. During its ve… — JAMB UTME

A rocket carries a payload of mass $25\text{ kg}$ resting on a spring balance. During its vertical ascent, the spring balance indicates a reading of $350\text{ N}$ . Taking the acceleration due to gravity as $g = 10\text{ m s}^{-2}$ , what is the magnitude of the upward acceleration of the rocket in $\text{m s}^{-2}$ ?

Answer: 4 m s^-2

Answer

The upward acceleration of the rocket is

4.0\text{ m s}^{-2}

When an object of mass

m

accelerates upward at rate

a

, the scale must exert an upward force

R

that overcomes the weight

mg

and provides net acceleration

ma

, such that

R = m(g + a)

. Substituting

R = 350\text{ N}

m = 25\text{ kg}

, and

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

yields

350 = 25(10 + a)

, which simplifies to

a = 4.0\text{ m s}^{-2}

Step-by-Step Solution

Formulate the equation of motion for apparent weight during upward acceleration

R - mg = ma \implies R = m(g + a)

The spring balance supports the mass against gravity while simultaneously providing the force for upward acceleration.

Substitute the given numerical parameters into the relation

350 = 25(10 + a)

The measured reading

R = 350\text{ N}

, mass

m = 25\text{ kg}

, and standard gravity

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

are supplied.

Solve the algebraic equation for the rocket's acceleration

a

a = 4.0\text{ m s}^{-2}

Dividing

350\text{ N}

25\text{ kg}

gives an effective total acceleration of

14\text{ m s}^{-2}

; subtracting

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

isolates the upward acceleration

a

Key Concept

Apparent Weight and Mass Measurement in Accelerating Frames

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