Calculating Momentum with Time: A Free Fall Problem

[kriegera]

Homework Statement

A body of mass 50 kg is allowed to fall freely under the action of gravity. Calculate the momentum it possesses after 5 seconds

Homework Equations

P=mv
F=ma

The Attempt at a Solution

I'm thinking we're really looking for how force affects momentum here? Since (F=ma) and acceleration is just how velocity changes over time would we use:
F = m * v/t
and then replace v with a =
F=(50)(9.81)/5 = 98.10 J

Is this correct?

 

[radou]

As you mentioned, momentum is defined as p = mv. v varies with t. What is the velocity of the mass during its' free fall?

 

[kriegera]

As you mentioned, momentum is defined as p = mv. v varies with t. What is the velocity of the mass during its' free fall?

v = vi- gt =
0-(-9.81)(5) = 49.05 m/s
this is assuming initial velocity was 0 which i don't think we can really assume.
Would we then insert that value:
F = m * v/t
F=(50)(49.05)/5 = 490.5 J

 

[radou]

v = vi- gt =
0-(-9.81)(5) = 49.05 m/s
this is assuming initial velocity was 0 which i don't think we can really assume.

Of course we can. :)

Would we then insert that value:
F = m * v/t
F=(50)(49.05)/5 = 490.5 J

So, you got the velocity after 5 seconds right.

Now, you only need to calculate the momentum, not the force. p = mv. you have the mass, and you have the velocity after 5 seconds.

 

[kriegera]

Now, you only need to calculate the momentum, not the force. p = mv. you have the mass, and you have the velocity after 5 seconds.

So then we would do:
P=mv = (50)(49.05) = 2,452.5 J
correct?

 

[radou]

Yes, you got it right.

 

[kriegera]

thank you!