# Calculate the final velocity of each cart after a collision

## Homework Statement

Cart 1 has a mass of 1.5 kg and is moving on a track at 36.5 cm/s [E] toward cart 2. The mass of cart 2 is 5 kg, and it is moving toward cart 1 at 42.8 cm/s [W]. The carts collide. The collision is cushioned by a Hooke's law spring, making it an elastic head-on collision. Calculate the final velocity of each cart after collision.

## The Attempt at a Solution

I plugged all my values into the head-on elastic collision formulas and I got vi1=84cm/s but the answer in the book is 3.15cm/s. I am really sure I have the right answer. Is there a mistake in the book?

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gneill
Mentor
I'm not liking any of the answers, yours or the book's (although yours looks somewhat better )

Can you show your work in detail?

Last edited:
Samy_A
Homework Helper

## Homework Statement

Cart 1 has a mass of 1.5 kg and is moving on a track at 36.5 cm/s [E] toward cart 2. The mass of cart 2 is 5 kg, and it is moving toward cart 1 at 42.8 cm/s [W]. The carts collide. The collision is cushioned by a Hooke's law spring, making it an elastic head-on collision. Calculate the final velocity of each cart after collision.

## The Attempt at a Solution

I plugged all my values into the head-on elastic collision formulas and I got vi1=84cm/s but the answer in the book is 3.15cm/s. I am really sure I have the right answer. Is there a mistake in the book?
Are you sure about the mass of cart 2?

The answer in the text I believe is incorrect I got -85cm/s like u

gneill
Mentor
The answer in the text I believe is incorrect I got -85cm/s like u
Can you show your work in detail? (I'm not disagreeing or agreeing with your conclusion, but we don't simply confirm/deny answers here).

haruspex
Homework Helper
Gold Member
The book answer would be correct if either cart 1 had a mass of 15kg or cart 2 a mass of .5kg.

• gneill
neilparker62
Homework Helper
The elastic collision impulse (calculated using formula Δp=2μΔv) is 1.83 Ns. Can be subtracted from the pre-collision momentum of each cart to find the final momentum and hence velocity. Seems to agree - more or less - with answer of -84 (-85) cm/s obtained by OP and PhysicsFailure123 (for Cart 1).

haruspex
Homework Helper
Gold Member
The elastic collision impulse (calculated using formula Δp=2μΔv) is 1.83 Ns. Can be subtracted from the pre-collision momentum of each cart to find the final momentum and hence velocity. Seems to agree - more or less - with answer of -84 (-85) cm/s obtained by OP and PhysicsFailure123 (for Cart 1).
I think it is fairly clear there is either an extra decimal point or, more likely, a missing one in the given data. See post #6.

• neilparker62
neilparker62
Homework Helper
I think it is fairly clear there is either an extra decimal point or, more likely, a missing one in the given data. See post #6.
Yes, if we take cart 1 to have mass 15kg , then the collision impulse Δp will be $594.75 \times 10^{-2}Ns$ and subtracting this from the initial momentum of cart 1 will lead to the book answer of 3.15cm/s (west) for final velocity of cart 1.