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Answer :
To determine which scenario requires more work, we can calculate the work done in both cases.
Scenario A: Pushing a box
- The force applied is 115 Newtons.
- The distance over which the box is pushed is 15 meters.
To calculate the work done, we use the formula:
[tex]\[ \text{Work} = \text{Force} \times \text{Distance} \][/tex]
So, for pushing the box:
[tex]\[ \text{Work}_A = 115 \, \text{N} \times 15 \, \text{m} = 1725 \, \text{Joules} \][/tex]
Scenario B: Lifting a mass
- The mass being lifted is 20 kilograms.
- The distance the mass is lifted is 10 meters.
- The force needed to lift the mass is equal to the gravitational force on it, which is the mass times the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 meters per second squared.
First, calculate the force needed to lift the mass:
[tex]\[ \text{Force}_B = \text{mass} \times \text{gravity} = 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N} \][/tex]
Then, calculate the work done in lifting the mass:
[tex]\[ \text{Work}_B = \text{Force}_B \times \text{Distance}_B = 196 \, \text{N} \times 10 \, \text{m} = 1960 \, \text{Joules} \][/tex]
Comparison:
- Work required for pushing the box (Scenario A): 1725 Joules
- Work required for lifting the mass (Scenario B): 1960 Joules
Since 1960 Joules (Scenario B) is greater than 1725 Joules (Scenario A), lifting the 20 kg mass a distance of 10 meters requires more work. Thus, Option B requires more work.
Scenario A: Pushing a box
- The force applied is 115 Newtons.
- The distance over which the box is pushed is 15 meters.
To calculate the work done, we use the formula:
[tex]\[ \text{Work} = \text{Force} \times \text{Distance} \][/tex]
So, for pushing the box:
[tex]\[ \text{Work}_A = 115 \, \text{N} \times 15 \, \text{m} = 1725 \, \text{Joules} \][/tex]
Scenario B: Lifting a mass
- The mass being lifted is 20 kilograms.
- The distance the mass is lifted is 10 meters.
- The force needed to lift the mass is equal to the gravitational force on it, which is the mass times the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 meters per second squared.
First, calculate the force needed to lift the mass:
[tex]\[ \text{Force}_B = \text{mass} \times \text{gravity} = 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N} \][/tex]
Then, calculate the work done in lifting the mass:
[tex]\[ \text{Work}_B = \text{Force}_B \times \text{Distance}_B = 196 \, \text{N} \times 10 \, \text{m} = 1960 \, \text{Joules} \][/tex]
Comparison:
- Work required for pushing the box (Scenario A): 1725 Joules
- Work required for lifting the mass (Scenario B): 1960 Joules
Since 1960 Joules (Scenario B) is greater than 1725 Joules (Scenario A), lifting the 20 kg mass a distance of 10 meters requires more work. Thus, Option B requires more work.
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