How Does Elevator Motion Affect Work Done by Forces?

In summary, the question involves a person in an elevator moving at a constant speed of 4.0 m/s for 5.0 s. The task is to calculate the work done by the normal force and the force of gravity on the person. If the elevator were moving down at the same speed and time, the displacement would be the same but the signs would change. The calculation for the work done by the normal force involves finding the displacement and equating the normal force to the force of gravity. The given answer of 12 kJ may not be correct and a different approach may be needed.
  • #1
Enduro
4
0
1. Homework Statement

the question is:
A 62 kg person in an elevator is moving up at a constant
speed of 4.0 m/s for 5.0 s. T / I C

(b) Calculate the work done by the normal force on the person.
(c) Calculate the work done by the force of gravity on the
person.
(d) How would your answers change if the elevator were
moving down at 4.0 m/s for 5.0 s?


2. Homework Equations
W= F x Δd

and i think

Δd= (vf + vi/2)Δt
fg=m.g
3. The Attempt at a Solution

for b) i did Δd= (vf + vi/2)Δt and got displacement which is 10 m and then i did fn=fg since fnet is 0 which means that they have the same force. and for that i got 607.6 N

p.s the answer in the back is 12 kJ which i don't get?
 
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  • #2
At constant velocity v, what is displacement d over time t?
 
  • #3
Enduro said:
1. Homework Statement

the question is:
A 62 kg person in an elevator is moving up at a constant
speed of 4.0 m/s
for 5.0 s. T / I C

(b) Calculate the work done by the normal force on the person.
(c) Calculate the work done by the force of gravity on the
person.
(d) How would your answers change if the elevator were
moving down at 4.0 m/s for 5.0 s?


2. Homework Equations
W= F x Δd

and i think

Δd= (vf + vi/2)Δt
fg=m.g
3. The Attempt at a Solution

for b) i did Δd= (vf + vi/2)Δt and got displacement which is 10 m and then i did fn=fg since fnet is 0 which means that they have the same force. and for that i got 607.6 N

p.s the answer in the back is 12 kJ which i don't get?

The lift was moving at a constant speed, so calculating displacement is much simpler than the way you did it - and your method gives the wrong answer because you assumed it started out at 0 m/s.
This 5 second interval is presumably a middle interval of the whole journey.
The lift gains speed - then travels at constant speed - then slows down and stops. The 5 sec interval is entirely in the middle section.
 
  • #4
Enduro said:
1. Homework Statement

the question is:
A 62 kg person in an elevator is moving up at a constant
speed of 4.0 m/s for 5.0 s. T / I C

(b) Calculate the work done by the normal force on the person.
(c) Calculate the work done by the force of gravity on the
person.
(d) How would your answers change if the elevator were
moving down at 4.0 m/s for 5.0 s?


2. Homework Equations
W= F x Δd

and i think

Δd= (vf + vi/2)Δt
fg=m.g
3. The Attempt at a Solution

for b) i did Δd= (vf + vi/2)Δt and got displacement which is 10 m and then i did fn=fg since fnet is 0 which means that they have the same force. and for that i got 607.6 N

p.s the answer in the back is 12 kJ which i don't get?
I believe you meant Δd= [(vf + vi)/2)]Δt. If the speed is constant, vf and vi are the same. Try again.
 
  • #5


I would first commend the student for correctly using the equations for work and displacement. However, I would suggest that they also consider the direction of the forces and displacement in their calculations. For part (b), the normal force is acting in the opposite direction of the displacement, so the work done by the normal force would be negative. Similarly, for part (c), the force of gravity is acting in the same direction as the displacement, so the work done by gravity would be positive. This leads to the correct answer of 12 kJ for part (b).

For part (d), if the elevator were moving down, the direction of the forces and displacement would be reversed, resulting in a positive work done by the normal force and a negative work done by gravity. This would lead to the same final answer of 12 kJ. Overall, it is important to consider the direction of forces and displacement in order to accurately calculate work done in a system.
 

Related to How Does Elevator Motion Affect Work Done by Forces?

What is the difference between kinematics and dynamics?

Kinematics is the study of the motion of objects without considering the forces that cause the motion. It focuses on concepts such as displacement, velocity, and acceleration. On the other hand, dynamics is the study of the forces that cause motion. It involves concepts such as Newton's Laws of Motion and how they apply to different situations.

What is the importance of studying kinematics and dynamics?

Studying kinematics and dynamics is important because it helps us understand and predict the motion of objects in our world. This knowledge is crucial in fields such as engineering, physics, and robotics, as it allows us to design and build machines and structures that move in a safe and efficient manner.

What is the difference between linear and rotational motion?

Linear motion is when an object moves along a straight line, while rotational motion is when an object rotates or spins around a fixed axis. Linear motion is described by displacement, velocity, and acceleration, while rotational motion is described by angular displacement, angular velocity, and angular acceleration.

What is the role of vectors in kinematics and dynamics?

Vectors are essential in kinematics and dynamics because they represent both the magnitude and direction of a physical quantity, such as velocity or force. In kinematics, vectors are used to describe the motion of an object, while in dynamics, they are used to represent the forces that cause the motion.

How does Newton's Laws of Motion apply to kinematics and dynamics?

Newton's Laws of Motion are fundamental principles that govern the motion of objects in both kinematics and dynamics. The first law states that an object will remain at rest or in motion with a constant velocity unless acted upon by a net external force. The second law relates the net force acting on an object to its acceleration, while the third law states that for every action, there is an equal and opposite reaction.

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