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A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?
- a)400 N
- b)800 N
- c)1000 N
- d)1200 N
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A person who weighs 800 N steps onto a scale that is on the floor of a...
The person exerts a downward force on the scale, and the scale pushes up on the person with an equal (but opposite) force, FN. Thus, the scale reading is FN, the magnitude of the normal force.
FN – FW = ma ⇒ FN – mg = ma
⇒ FN = ma + mg = m (a + g) = (W/g) (a + g) = (800/10) (10 + 5)
FN = 1200 N
Most Upvoted Answer
A person who weighs 800 N steps onto a scale that is on the floor of a...
Given information:
Weight of the person = 800 N
Acceleration of the elevator = 5 m/s^2
To find:
What will the scale read when the person steps onto it?
Solution:
When the person stands on the scale, the scale measures the normal force exerted by the person's weight. The normal force is equal to the weight of the person.
In this case, the person's weight is 800 N. However, due to the acceleration of the elevator, an additional force is acting on the person. This force is equal to the mass of the person multiplied by the acceleration of the elevator (Newton's second law).
To calculate the mass of the person, we can use the formula:
Weight = Mass x Gravity
800 N = Mass x 9.8 m/s^2
Mass = 800 N / 9.8 m/s^2
Mass ≈ 81.63 kg
Now, we can calculate the additional force acting on the person:
Force = Mass x Acceleration
Force = 81.63 kg x 5 m/s^2
Force = 408.15 N
The total force exerted on the person is the sum of their weight and the additional force:
Total Force = Weight + Additional Force
Total Force = 800 N + 408.15 N
Total Force ≈ 1208.15 N
Since the scale measures the normal force exerted by the person's weight, the scale will read a value equal to the total force exerted on the person, which is approximately 1208.15 N.
Therefore, the correct answer is option D) 1200 N.
Weight of the person = 800 N
Acceleration of the elevator = 5 m/s^2
To find:
What will the scale read when the person steps onto it?
Solution:
When the person stands on the scale, the scale measures the normal force exerted by the person's weight. The normal force is equal to the weight of the person.
In this case, the person's weight is 800 N. However, due to the acceleration of the elevator, an additional force is acting on the person. This force is equal to the mass of the person multiplied by the acceleration of the elevator (Newton's second law).
To calculate the mass of the person, we can use the formula:
Weight = Mass x Gravity
800 N = Mass x 9.8 m/s^2
Mass = 800 N / 9.8 m/s^2
Mass ≈ 81.63 kg
Now, we can calculate the additional force acting on the person:
Force = Mass x Acceleration
Force = 81.63 kg x 5 m/s^2
Force = 408.15 N
The total force exerted on the person is the sum of their weight and the additional force:
Total Force = Weight + Additional Force
Total Force = 800 N + 408.15 N
Total Force ≈ 1208.15 N
Since the scale measures the normal force exerted by the person's weight, the scale will read a value equal to the total force exerted on the person, which is approximately 1208.15 N.
Therefore, the correct answer is option D) 1200 N.
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A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?a)400 Nb)800 Nc)1000 Nd)1200 NCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?a)400 Nb)800 Nc)1000 Nd)1200 NCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?a)400 Nb)800 Nc)1000 Nd)1200 NCorrect answer is option 'D'. Can you explain this answer?.
A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?a)400 Nb)800 Nc)1000 Nd)1200 NCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?a)400 Nb)800 Nc)1000 Nd)1200 NCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?a)400 Nb)800 Nc)1000 Nd)1200 NCorrect answer is option 'D'. Can you explain this answer?.
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A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?a)400 Nb)800 Nc)1000 Nd)1200 NCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?a)400 Nb)800 Nc)1000 Nd)1200 NCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?a)400 Nb)800 Nc)1000 Nd)1200 NCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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