How does the loader's linear momentum change after turning south?

[cassie123]

Homework Statement

A 15,000 kg loader traveling east at 20 km/h turns south and travels at 25 km/h. Calculate the change in the loader’s
a. kinetic energy.
b. linear momentum.

Homework Equations

KE=(1/2)mv^2
p=mv
p(i)=p(f) : I am assuming I can ignore gravity

The Attempt at a Solution

I know there is already a thread for this problem but I am having trouble understanding how to describe the change in linear momentum,

I feel okay with part a:
a) 20km/hr = 5.56m/s
25km/hr=6.94 m/s

KE2-KE1
1/2mv2^2 - 1/2mv1^2
1/2 (15000)(6.94)^2 - 1/2(15000)(5.56)^2
361227-231852
129375J

But for part b I am confused as to what to quantify as the change in linear momentum. So far I have:

b)
p(east) = mva
(15000kg)(5.56m/s)
83400 kg*m/s

p(south) = mvb
(15000kg)(6.94m/s)
104100 kg*m/s

And then I used pythagorean and inverse tan to find a resultant momentum of 1.3 * 10^5 with an angle of 51 degrees south of east.

Is this my final answer? Do I need to subtract this from the initial momentum in the easterly direction? Why or why not?

Any help is appreciated, thanks!

 

[Dr. Courtney]

pi is not equal to pf.

You have the external forces of the wheels and the road.

You need to compute the initial and final momentum vectors and subtract them (as vectors).

 

[cassie123]

Dr. Courtney, thanks for your answer. I'm not sure I understand where to begin following your suggestions

 

[SammyS]

Homework Statement

A 15,000 kg loader traveling east at 20 km/h turns south and travels at 25 km/h. Calculate the change in the loader’s
a. kinetic energy.
b. linear momentum.

Homework Equations

KE=(1/2)mv^2
p=mv
p(i)=p(f) : I am assuming I can ignore gravity

The Attempt at a Solution

I know there is already a thread for this problem but I am having trouble understanding how to describe the change in linear momentum,

I feel okay with part a:
...

But for part b I am confused as to what to quantify as the change in linear momentum. So far I have:

b)
p(east) = mva
(15000kg)(5.56m/s)
83400 kg*m/s

p(south) = mvb
(15000kg)(6.94m/s)
104100 kg*m/s

And then I used pythagorean and inverse tan to find a resultant momentum of 1.3 * 10^5 with an angle of 51 degrees south of east.

Is this my final answer? Do I need to subtract this from the initial momentum in the easterly direction? Why or why not?

Any help is appreciated, thanks!

Hello cassie123. Welcome to PF!

It appears that you're adding the two momentum vectors. To find the change, you should subtract. Right?

 

[cassie123]

Hello cassie123. Welcome to PF!

It appears that you're adding the two momentum vectors. To find the change, you should subtract. Right?

Thanks SammyS!

Yes, that makes more sense that I should subtract.

Can I just subtract the south momentum from the east or does the directionality mess that up? Or I think I could also use the change in velocity multiplied by mass. I am getting confused thinking about whether I need to resolve vectors, since they are already on the coordinate plane. And to me it makes sense that the change in direction would be 90 degrees from east to south but I'm having a hard time knowing how to handle this!

 

[SammyS]

Thanks SammyS!

Yes, that makes more sense that I should subtract.

Can I just subtract the south momentum from the east or does the directionality mess that up? Or I think I could also use the change in velocity multiplied by mass. I am getting confused thinking about whether I need to resolve vectors, since they are already on the coordinate plane. And to me it makes sense that the change in direction would be 90 degrees from east to south but I'm having a hard time knowing how to handle this!

If you want to find how much something has changed, you take the final value and subtract the initial value from that. In other words, subtract the initial (east) from the final (south).

 

[cassie123]

If you want to find how much something has changed, you take the final value and subtract the initial value from that. In other words, subtract the initial (east) from the final (south).

Maybe I'm overcomplicating it. Thanks again!