Lift relative velocity question.

In summary, we are looking at a problem where a man throws a ball vertically upward from a lift moving upward with a uniform acceleration 'a'. The ball comes back to the man after a time 't'. By substituting values 'v', 't' and a+g as acceleration in the equation s=ut+1/2gt^2, we can show that a+g = 2v/t. This is done by considering it from the lift's frame of reference and taking into account the sign conventions of the accelerations. The informal explanation is that the upward acceleration of the elevator adds to the downward acceleration of gravity.
  • #1
takando12
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Homework Statement


From a lift moving upward with a uniform acceleration 'a', a man throws a ball vertically upward with a velocity v relative to the lift.The ball comes back to the man after a time 't' Show that a+g = 2v/t

Homework Equations


s=ut+1/2gt2

The Attempt at a Solution


I know this is a simple problem. By the substituting values 'v', 't' and a+g as acceleration in the above equation, i could get the answer. All of this is done by considering it from the lift's frame of reference. But I don't understand why we are adding g and a . SHouldn't we subtract them ? the ball goes up and down so must we subtract it the first time and add it the second? really confused.
 
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  • #2
takando12 said:
I know this is a simple problem. By the substituting values 'v', 't' and a+g as acceleration in the above equation, i could get the answer. All of this is done by considering it from the lift's frame of reference. But I don't understand why we are adding g and a . SHouldn't we subtract them ? the ball goes up and down so must we subtract it the first time and add it the second? really confused.
Yes, if one is computing the relative acceleration of two objects, one should take the difference of the two accelerations. But... take a look at the sign conventions here. The lift's acceleration is positive upward. The ball's acceleration (from gravity) is positive downward. Yes, you have to subtract. But before you subtract, you have give the two values the same sign convention. That means you have to negate one or the other. g-(-a) = g+a. That's the formal way to look at it.

The informal way to look at it is that the faster the elevator accelerates upward toward the ball, the faster the ball seems to accelerate downward toward the elevator. So the upward acceleration of the elevator adds to the downward acceleration of gravity.
 
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thank you...i forgot the signs completely. And the informal explanation tops it nicely.
 

Related to Lift relative velocity question.

What is lift relative velocity?

Lift relative velocity refers to the velocity of an aircraft relative to the surrounding air. It is the difference between the airspeed of the aircraft and the airspeed of the surrounding air. This is an important factor in determining the amount of lift that the aircraft generates.

How does lift relative velocity affect an aircraft's lift?

The lift generated by an aircraft is directly proportional to its lift relative velocity. As the lift relative velocity increases, so does the amount of lift generated. This is because a higher relative velocity results in a greater difference in air pressure between the top and bottom surfaces of the aircraft's wings, creating a larger lifting force.

What factors can affect lift relative velocity?

The lift relative velocity of an aircraft can be affected by several factors, such as the weight, shape, and air density of the aircraft. Additionally, changes in the surrounding air, such as wind speed and direction, can also impact the lift relative velocity of an aircraft.

How do pilots control lift relative velocity during flight?

Pilots can control lift relative velocity by adjusting the airspeed of the aircraft. By increasing or decreasing the airspeed, pilots can change the lift relative velocity and thus, the amount of lift being generated. This is an important skill for pilots to master in order to maintain a safe and stable flight.

Why is understanding lift relative velocity important for aircraft design?

Understanding lift relative velocity is crucial for aircraft design as it allows engineers to design and build aircraft with optimal lift capabilities. By considering factors such as weight, shape, and air density, engineers can design aircraft that can generate enough lift at various speeds to achieve safe and efficient flight. Additionally, understanding lift relative velocity is important for making informed decisions during flight, such as when to adjust airspeed for different flight conditions.

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