Finding Velocity of a dropped ball

In summary, the conversation discusses the calculation of the speed of a baseball when it hits the ground after being released from a height of 3.5m. The chosen system is the baseball and the Earth, and the energy principle is used to solve for the final velocity. The total energy of the system is zero and the final kinetic energy is equal to the initial potential energy. By setting these equal and solving for the velocity, the answer is found to be 8.3m/s.
  • #1
cowmoo32
122
0
A baseball of mass .025kg is released at rest from a location 3.5m above the ground. You will calculate its speed at the instant it hits the ground.

Choose a sysem to analyze, and list the objects in your system.
I chose the baseball and the Earth as the system

Write out the energy principle as it applies to the system you have chosen. Solve for the speed of the baseball when it hits the ground
Here's where I'm lost. The baseball has kinetic energy (1/2mv^2), and the Earth is pulling down on it (-9.8*m), but I'm not sure how to arrive at the answer. According to the key, the answer is 8.3m/s.
 
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  • #2
If you are supposed to solve this problem using conservation of energy, you need to know the potential energy (PE) of the ball before it is dropped. How much energy did it take to initially lift the ball from the ground to the height h?
 
  • #3
Wouldnt that be M*G*D? .025*9.8*3.5 = .8575
 
  • #4
Yep. And what is the total energy (TE) of the system? What can you say about it? How does that help you solve for the ball's final velocity?
 
  • #5
Total energy has to equal zero.

K+U+G=0
(.5mv^2)+.8575-(9.8*m)=0
correct?
or would it be
K+G=U?
 
  • #6
I'm guessing that you mean KE for K, but what are U and G? I use TE=KE+PE myself.
 
  • #7
oh, G=gravity U=potential energy K=kinetic energy
 
  • #8
cowmoo32 said:
oh, G=gravity U=potential energy K=kinetic energy

Gravity is not an energy. Different units, different concept. All the energies in the equation should have units of joules.
 
  • #9
ahhh...ok.I'm still not sure how to find velocity though. If I have KE+PE=TE, I'm still left with 2 variables. Because my velocity is unknown for KE, then I don't have a number for TE.
 
  • #10
moo, the concept here is that the TE does not change when you drop a ball. What is lost from the initial PE is gained in the KE. What is the initial PE from lifting the ball from the ground to a height h? Be sure to include units for all quantities in that equation that you will write. Then assuming that all that PE is lost and converted to KE in the fall, what is the final KE? What does that mean the final v is? I got to go now. You're almost there.
 
  • #11
PE of the ball is equal to the KE of the ball as it hits the ground
 
  • #12
fffff said:
PE of the ball is equal to the KE of the ball as it hits the ground

That's not stated very well. More accurately, the TE of the ball is all PE when the velocity is zero (at the top), and the TE is all KE just before it hits the ground.
 

Related to Finding Velocity of a dropped ball

1. What is the equation for finding velocity of a dropped ball?

The equation for finding the velocity of a dropped ball is v = gt, where v is the velocity in meters per second (m/s), g is the acceleration due to gravity (9.8 m/s²), and t is the time in seconds.

2. How do you measure the time for a dropped ball?

The time for a dropped ball can be measured using a stopwatch or a timer. The timer should be started as soon as the ball is released and stopped as soon as the ball hits the ground.

3. Can air resistance affect the velocity of a dropped ball?

Yes, air resistance can affect the velocity of a dropped ball. As the ball falls, it experiences air resistance, which slows it down. This effect is more noticeable for larger and less dense objects.

4. Is the velocity of a dropped ball affected by the height from which it is dropped?

Yes, the velocity of a dropped ball is affected by the height from which it is dropped. According to the equation v = gt, the velocity is directly proportional to the height from which the ball is dropped. This means that the higher the drop height, the greater the velocity of the ball when it reaches the ground.

5. Can the velocity of a dropped ball be greater than the initial velocity?

No, the velocity of a dropped ball cannot be greater than the initial velocity. The initial velocity of a dropped ball is always zero, as it is released from rest. The maximum velocity that the ball can achieve is when it reaches the ground, and it will be equal to the velocity just before impact.

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