Find the maximum speed of the elevato

In summary, A person of mass mp stands on a scale in an elevator of mass me, which reads the magnitude of the force F exerted on it from above in a downward direction. The elevator starts at rest and moves upward, coming to rest again after a period of time t_0. The downward acceleration of gravity is g. The acceleration of the elevator during this period is given by ay(t)=α−2αt_0t. Part a asks for the maximum speed of the elevator, which is 1/4*α*t_0. Part b asks for the total distance traveled by the elevator, which can be found by integrating the velocity function with respect to time from t=0 to t=t_0,
  • #1
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Homework Statement



A person of mass mp stands on a scale in an elevator of mass me . The scale reads the magnitude of the force F exerted on it from above in a downward direction. Starting at rest at t=0 the elevator moves upward, coming to rest again at time t=t_0. The downward acceleration of gravity is g . The acceleration of the elevator during this period is shown graphically above and is given analytically by ay(t)=α−2αt_0t

a) Find the maximum speed of the elevator. Express your answer in terms of α and t0

b) Find the total distance traveled by the elevator. Express your answer in terms of α and t0 (enter alpha for α and t_0 for t0)

Homework Equations





The Attempt at a Solution



I got part a right (answer is 1/4*alpha*t_0) but I don't know how to get b I tried integrating the velocity with repsect to t with the limits of t_0 and 0 and I got 1/4*a*t_0^2, but that is not right. Can someone please tell me what I;m doing wrong?
 
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  • #2
What is the velocity function and how do you integrate it?
 

1. What is the maximum speed of the elevator?

The maximum speed of the elevator depends on various factors such as the type of elevator, weight limit, and mechanical limitations. It is typically between 500 feet per minute (FPM) to 2000 FPM.

2. How is the maximum speed of an elevator determined?

The maximum speed of an elevator is determined by the elevator manufacturer and is based on the weight limit and the type of elevator mechanism used. It is also regulated by safety codes and standards.

3. Can the maximum speed of an elevator be changed?

In most cases, the maximum speed of an elevator cannot be changed as it is set by the manufacturer and is regulated by safety standards. Altering the speed of an elevator can also pose safety risks and is not recommended.

4. What are the safety considerations for determining the maximum speed of an elevator?

The maximum speed of an elevator is determined with safety in mind. Factors such as acceleration and deceleration rates, emergency stopping procedures, and weight limits are taken into consideration to ensure the safety of passengers.

5. Can the maximum speed of an elevator affect its efficiency?

Yes, the maximum speed of an elevator can affect its efficiency. A higher speed may result in more wear and tear on the elevator mechanism, leading to increased maintenance and energy costs. It is important to find a balance between speed and efficiency when determining the maximum speed of an elevator.

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