A 50-kg object was dropped from a height of 2 meters from water level

In summary, a 50-kg object was dropped from a height of 2 meters into an open water-tank with a hole 3 meters below the water's surface. The area of the water tank is 1.5 square meters and the diameter of the hole is 2 square millimeters. The question asks for the maximum speed of water exiting the tank, given a mini impact time of 0.02 seconds. The solution requires deriving an equation from physics principles and considering the behavior of the falling mass.
  • #1
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Homework Statement


A 50-kg object was dropped from a height of 2 meters from water level of tank. The open water-tank has a hole 3 meters below water's surface. area of water tank is 1.5 sq m and diameter of hole is 2 sq mm. What is the max speed of water exiting the tank if the mini impact time is .02 seconds?


Homework Equations



What is the equation?

The Attempt at a Solution


What is the equation?
 
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  • #2


This is not one of those cases where there is a standard equation - you have to derive it from the physics.

What kinds of physics do you think should apply here?

Note: I don't know what the falling mass is supposed to do.
Does it hit the surface of the water?
If so, does it float or sink?
If not: did it start below water-level, or is it next to the tank?
 

1. What is the initial velocity of the object when it is dropped from a height of 2 meters?

The initial velocity of the object can be calculated using the equation v = √(2gh), where v is the initial velocity, g is the acceleration due to gravity (9.8 m/s^2), and h is the height from which the object is dropped. Plugging in the values, the initial velocity is approximately 6.26 m/s.

2. What is the final velocity of the object when it reaches the water level?

The final velocity of the object can be calculated using the equation v^2 = u^2 + 2gh, where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and h is the height from which the object was dropped. Since the object is dropped from rest (u = 0), the final velocity is equal to the initial velocity, which is approximately 6.26 m/s.

3. How long does it take for the object to reach the water level?

The time it takes for the object to reach the water level can be calculated using the equation t = √(2h/g), where t is the time, h is the height from which the object is dropped, and g is the acceleration due to gravity. Plugging in the values, the time taken is approximately 0.64 seconds.

4. What is the kinetic energy of the object when it reaches the water level?

The kinetic energy of the object can be calculated using the equation KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the object, and v is the final velocity. Plugging in the values, the kinetic energy of the object is approximately 980 J.

5. What is the impact force of the object when it hits the water?

The impact force of the object can be calculated using the equation F = m * a, where F is the impact force, m is the mass of the object, and a is the acceleration due to gravity. Since the object hits the water with a velocity of 6.26 m/s, the deceleration due to gravity is also 6.26 m/s^2. Therefore, the impact force is approximately 313 N.

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