Momentum - velocity due to height

In summary, the momentum of a 0.20 kg ball thrown straight up with an initial velocity of 19 m/s is 0 when at its maximum height. Halfway to its maximum height, the momentum is equal to 131.66. This is found by using the equation mgh = 1/2mv^2 and solving for v. The conservation laws of energy and momentum can be used to solve for the velocity at different points of the ball's motion. It is important to work with algebra as long as possible to avoid mistakes.
  • #1
ngorecki
37
0

Homework Statement



A 0.20 kg ball is thrown straight up into the air with an initial speed of 19 m/s. Find the momentum of the ball at the following locations.

(a) at its maximum height
(b) halfway to its maximum height

Variable:
ball = .2kg
Vi = 19 m/s

Homework Equations



p = mv

The Attempt at a Solution



a) since the object is at max height the velocity is 0. therefore momentum is also 0.
b)This is where I ger lost...
I tried using the equation for momentum but I am not sure on how to solve for velocity.
My teacher said something about height being = to v^2 but he said this quickly and not sure what the usefulness of that is...

It would be greatly appreciated if I could get help ASAP
 
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  • #2
During ascent, gravity acts on the ball. As a result, the ball's vertical momentum is not conserved. What is conserved?
 
  • #3
Total velocity is conserved...?
 
  • #4
How many laws of conservation have you heard of?
 
  • #5
energy and momentum
 
  • #6
ngorecki said:
energy and momentum
Good. I've explained why you can't using conservation of momentum here, so that leaves ...?
 
  • #7
Alright so
mgh = 1/2mv^2
Cancel mass
gh = 1/2v^2
9.8(h) = .5(19)^2
h = 1768.9

Then mgh(.5h) = 1/2mv^2
Cancel mass
9.8(.5*1768.9) = 1/2v^2
8667.61 = 1/2v^2
17335.22 = v^2
131.66 = v
 
  • #8
ngorecki said:
Alright so
mgh = 1/2mv^2
Cancel mass
gh = 1/2v^2
9.8(h) = .5(19)^2
h = 1768.9

Then mgh(.5h) = 1/2mv^2
Cancel mass
9.8(.5*1768.9) = 1/2v^2
8667.61 = 1/2v^2
17335.22 = v^2
131.66 = v
I strongly urge you to get into the habit of working with the algebra as long as possible, only plugging numbers in right at the end. It will help you avoid mistakes, help spot mistakes, and help others follow what you're doing.
Your answer is clearly wrong since it exceeds the initial velocity.
 

1. What is momentum?

Momentum is a measure of an object's tendency to continue moving in a straight line at a constant speed. It is calculated by multiplying the object's mass by its velocity.

2. How is momentum related to velocity?

Momentum and velocity are directly proportional to each other. This means that as an object's velocity increases, its momentum also increases.

3. How does height affect an object's velocity and momentum?

Height has a direct effect on an object's velocity and momentum. As an object gains height, it also gains potential energy. When this potential energy is converted into kinetic energy, the object's velocity and momentum increase.

4. Can momentum be negative?

Yes, momentum can be negative. This occurs when an object is moving in the opposite direction of its chosen positive direction. In this case, the momentum would have a negative sign to indicate its direction.

5. What is the relationship between momentum and mass?

Mass and momentum are directly proportional to each other. This means that as an object's mass increases, its momentum also increases. This can be observed in collisions, where a heavier object will have a greater momentum than a lighter object with the same velocity.

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