A student with a mass of 58kg runs up three flights of stairs. The student has gone a vertical distance of 6m. Determine the amount of work done (In Joules) by the student to elevate his body to this height. Assume that his speed is constant and g = 9.81m/s2. Only put in the numerical value. Do not write the unit in your answer.

This is a short-answer question. Show all working on paper, including the relevant equations and units.

Question

A student with a mass of 58kg runs up three flights of stairs. The student has gone a vertical distance of 6m. Determine the amount of work done (In Joules) by the student to elevate his body to this height. Assume that his speed is constant and g = 9.81m/s2. Only put in the numerical value. Do not write the unit in your answer.

This is a short-answer question. Show all working on paper, including the relevant equations and units.

BlackTom AI · Accepted Answer

First, restate the problem in my own words to ensure understanding: a 58 kg student raises their body by a vertical distance of 6 m with constant speed up three flights of stairs, and we are asked to find the work done to elevate the body against gravity. Since speed is constant, the work done goes into increasing gravitational potential energy, which equals m g h.

Step 1: Identify the given quantities. Mass m = 58 kg, gravitational acceleration g = 9.81 m/s^2, vertical height h = 6 m.

Step 2: Write the formula for work against gravity. The work done by gravity (or by an external agent lifting the student) to raise the mass by height h is W = m g h.

Step 3: Perform the calculation. Compute g h first: 9.81 × 6 = 58.86. Then multiply by the mass: 58 × 58.86 = 58 × (60 − 1.14) which is 58 × 60 − 58 × 1.14 = 3480 − 66.12 ≈ 3413.88.

Step 4: Interpret the result. The numeric value obtained from W = m g h is 3413.88, representing the work done in the same energy units as g, m, and h imply, i.e., joules when using SI units. If you were comparing to a provided numerical answer, ensure the same g value and proper multiplication are used to avoid small discrepancies.

Step 5: Address the instruction about units. The derived quantity is a work value measured in joules; when presenting, you would typically write 3413.88, with the unit joules implied by the context. If a specific rounding rule is given (e.g., to two decimals), you would apply it accordingly.

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