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s.h_math s.h_math
wrote...
Posts: 33
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A month ago



Hi there, I was wondering if I could get help with this question. Thanks a lot Slight Smile

A 15.0 kg penguin waddling east at a velocity of 7.0 m/s collides with a stationary 10.0 kg penguin. After the collision the 15.0 kg penguin is traveling at a velocity Of 4.2 m/s 20.00 S of E.

a. What is the velocity of the 10.0 kg penguin after collision?

b. is this collision elastic or inelastic?
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wrote...
Staff Member
A month ago
Part A:

Using momentum conservation we have:

Direction \(x\):

(15) (7.0) + 0 = (15) (4.2) cos (-20 °) + (10) v₂ (f) cosθ

(10) v₂ (f) cosθ = (15) (7.0) - (15) (4.2) cos (-20 °) ... (Eq 1)

Direction \(y\):

0 + 0 = (15) (4.2) sin (-20 °) + (10) v₂ (f) sinθ

(10) v₂ (f) sinθ = - (15) (4.2) sin (-20 °) ... (Eq 2)

We divide both equations (1) and (2):

Left side:

(10) v₂ (f) sinθ / (10) v₂ (f) cosθ = tanθ

Right side:

- (15) (4.2) sin (-20 °) / (15) (7.0) - (15) (4.2) cos (-20 °)

Clearing the angle we have:

θ = tan⁻¹ [ - (15) (4.2) sin (-20 °) / (15) (7.0) - (15) (4.2) cos (-20 °) ]

θ = 25 °

We use any of the equations to find the speed.

From (2) we have:

(10) v₂ (f) sinθ = - (15) (4.2) sin (-20 °)

v₂ = - (15) (4.2) sin (-20 °) / (10) sin25 °

Answer:

v₂ = 5.1m / s

Note: θ = 25 ° (direction is in the first quadrant, north of east)

Part B:

Initial kinetic energy: K (i) = 0.5 (15) (7.0) ² = 370J (rounded)

Final kinetic energy: KE (f) = 0.5 (15kg) (4.2m / s) ² + 0.5 (10kg) (5.1m / s) ² = 260J (rounded)

Answer:

A difference of 110J, so it was an inelastic collision.
- Master of Science in Biology
- Bachelor of Science (Biology)
- Bachelor of Education
wrote...
A month ago
Hey duddy it makes sense but could you write the initial equations to what we are plugging the numbers in? Thankss
wrote...
Staff Member
A month ago
The conservation of momentum formula goes like this:

total momentum before = total momentum after

linear momentum = mass * velocity

In other words: \(\rho =m\cdot v\)

I'll break down the first one for you, and hopefully you can apply it to the rest.

Recall:

Direction \(x\):

m*v + m*v = m*v + m*v
1..........2.........3....... ...4

in term 1: (15) (7.0)
in term 2: (10) (0) = 0
in term 3: (15) (4.2) cos (-20°)
in term 4: (10) v₂ (f) cosθ

how's that?
- Master of Science in Biology
- Bachelor of Science (Biology)
- Bachelor of Education
wrote...
A month ago
Yeah for sure thanks a lot!
wrote...
A month ago


you just need number 5?
wrote...
A month ago
Yeah, as it’s the only number circled.
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