- #1

aspodkfpo

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For 1 b) how did they get that equation? Is it wrong?

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- Thread starter aspodkfpo
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In summary: Oh right, this is inelastic so kinetic energy isn't conserved, but momentum is always conserved. Thus I can't determine v2 with energy formulas. Make an expression relating v1 to v2 through momentum.momentum is always conserved.... provided there is no net external force on the system.

- #1

aspodkfpo

- 148

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For 1 b) how did they get that equation? Is it wrong?

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- #2

DrClaude

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- #3

aspodkfpo

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DrClaude said:

What would the correct equation be? without an extra m/(m+M)?

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You are not expected to determine whether the formula is right or wrong. You are only asked whether the answer the formula gives to 1a is the same as your answer, and how you determined that.aspodkfpo said:What would the correct equation be? without an extra m/(m+M)?

- #5

aspodkfpo

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haruspex said:You are not expected to determine whether the formula is right or wrong. You are only asked whether the answer the formula gives to 1a is the same as your answer, and how you determined that.

DrClaude said:

I know what the question is asking for, I'm just curious about whether that formula is right/can be calculated.

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It is correct.aspodkfpo said:I know what the question is asking for, I'm just curious about whether that formula is right/can be calculated.

What is the velocity of the dart when it reaches the block?

What is the combined velocity when the dart is embedded in the block?

What is the KE of that?

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- #7

aspodkfpo

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haruspex said:It is correct.

What is the velocity of the dart when it reaches the block?

What is the combined velocity when the dart is embedded in the block?

What is the KE of that?

FL = 1/2 mv^2

FL = D x (friction coefficient) x (M+m)g

D= FL/((friction coefficient) x (M+m) g)

Where am I wrong?

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You are not taking into account the collision.aspodkfpo said:FL = 1/2 mv^2

FL = D x (friction coefficient) x (M+m)g

D= FL/((friction coefficient) x (M+m) g)

Where am I wrong?

It's a bit tricky because you don't know how long it takes for the dart to become stationary wrt the box, so assume that happens very quickly. I.e. treat it as three phases: acceleration of dart, dart and box coalesce, dart and box slide together.

- #9

aspodkfpo

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haruspex said:You are not taking into account the collision.

It's a bit tricky because you don't know how long it takes for the dart to become stationary wrt the box, so assume that happens very quickly. I.e. treat it as three phases: acceleration of dart, dart and box coalesce, dart and box slide together.

FL = 1/2 mu^2

= 1/2 (m+M) v^2

= D (friction coeff) x (m+M) g

I don't understand how to calculate the dart and box coalescing?

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How does one calculate any coalescence problem? Momentum!aspodkfpo said:FL = 1/2 mu^2

= 1/2 (m+M) v^2

= D (friction coeff) x (m+M) g

I don't understand how to calculate the dart and box coalescing?

- #11

aspodkfpo

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haruspex said:How does one calculate any coalescence problem? Momentum!

Oh right, this is inelastic so kinetic energy isn't conserved, but momentum is always conserved. Thus I can't determine v2 with energy formulas. Make an expression relating v1 to v2 through momentum.

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... provided there is no net external force on the system.aspodkfpo said:momentum is always conserved.

The purpose of this sample question is to test a student's understanding of projectile motion and collisions, as well as their ability to apply the laws of physics to real-world scenarios.

While the scenario may seem simplistic, it is meant to demonstrate the principles of projectile motion and collisions in a controlled environment. In real life, there may be other factors at play that could affect the outcome.

The use of a dart allows for a more streamlined and simplified calculation of the projectile's motion, making it easier for students to understand and solve the problem. In addition, the specific materials and dimensions of the dart and box have been carefully chosen to ensure a consistent and accurate result.

Yes, this question can be solved using various methods such as kinematic equations, conservation of momentum, and energy conservation. The important thing is to understand the underlying principles and apply them correctly to arrive at the correct solution.

This sample question is closely related to the topics of kinematics, dynamics, and energy conservation. It also serves as a good foundation for more complex problems involving collisions and projectile motion that may be encountered in the course.

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