Calculating Velocity & Displacement of a Dropped Object

In summary, The velocity of a 1 Kg object just before it lands on a stack of pillows from a helicopter at an altitude of 2000 meters is 200 m/s. It is suggested to use energy calculations due to the inclusion of a spring in the second part of the question. The total energy, which includes gravitational and kinetic energy, is conserved at both the point where the object is dropped and where it hits the pillows. The formula for the total energy is Etotal = Epotential + Ekinetic, where Epotential is the gravitational energy. To find the distance the object travels into the stack of pillows before coming to a full stop, the kinetic energy is set equal to the energy in the spring, which is
  • #1
Kaxa2000
71
0
A 1 Kg object is dropped from rest from a helicopter at an altitude
of 2000 meters. What is the velocity of the object just before it lands upon a thick bed of pillows? The top of the pillow stack is at zero altitude. If the restoring force
constant (spring constant) of the stack of pillows is 1 N/m, how far into the stack will the
object travel before it comes to a full stop? Neglect air resistance.
 
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  • #2


So you can start by calculating the final velocity. There are two ways to go here: one would be to use forces (Newton's laws, etc); and the other is using energies (conversion from potential to kinetic energy, etc).

Since the second part of the question includes a spring, I suggest you are supposed to use energies here?

So there are two relevant points: the point where the object is dropped and the point 2000 meters below it where it hits the pillows. As you know, the total energy
Etotal = Epotential + Ekinetic
is conserved (i.e. the same at these two points), where Epotential is the gravitational energy.
Can you give me the formulas for the two quantities on the right hand side and express them in given values and unknowns?
 
  • #3


Would it be

mgh + 1/2mv2

(1kg)(9.8m/s2)(2000m) + (1/2)(1kg)(v)2
 
  • #4


After you solve for v you get 200 m/s.

Do you set the KE = to the spring equation after that to find distance it goes into pillows?

1/2mv^2 = kX?
 
  • #5


almost--energy in a spring is of the same form=1/2kx^2 As written above you are equating energy and force.
 

Related to Calculating Velocity & Displacement of a Dropped Object

1. What is the formula for calculating velocity of a dropped object?

The formula for calculating velocity of a dropped object is: velocity (v) = (final velocity - initial velocity) / time. This is known as the average velocity formula.

2. How do you calculate displacement of a dropped object?

The formula for calculating displacement of a dropped object is: displacement (d) = (final position - initial position). This means subtracting the initial position from the final position.

3. What is the difference between velocity and speed?

Velocity and speed are often used interchangeably, but they have different meanings. Velocity is a vector quantity, meaning it has both magnitude and direction. Speed, on the other hand, is a scalar quantity and only refers to the magnitude of an object's motion.

4. How does air resistance affect the velocity and displacement of a dropped object?

Air resistance can have a significant impact on the velocity and displacement of a dropped object. As an object falls, it experiences air resistance, which acts in the opposite direction of its motion. This can cause the object to reach a terminal velocity, where the air resistance is equal to the force of gravity, resulting in a constant velocity. As a result, the displacement of the object will be limited and it will not continue to accelerate.

5. Can the velocity and displacement of a dropped object be affected by the object's mass?

Yes, the velocity and displacement of a dropped object can be affected by its mass. According to Newton's second law of motion, the greater the mass of an object, the more force is needed to accelerate it. Therefore, a heavier object will have a lower velocity and smaller displacement when dropped compared to a lighter object.

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