Calculating the velocity of a target and embedded projectile

[NewtonIsAmazing]

Homework Statement

A projectile of mass 100g, moving at a speed of 400m/s, collides with a stationary wooden target of mass 1.5kg which is free to move. The projectile enters the wooden target on impact and remains embedded in it.

Homework Equations

a) calculate the velocity of the target and embedded projectile immediately after the impact

b) calculate the average force of the impact, if the duration of the collision was 0.10 seconds

c) calculate the respective accelerations of the projectile and the target during the impact

The Attempt at a Solution

Attempt at a)

(0.1kg x 400m/s) + (1.5kg x 0m/s) = (0.1kg + 1.5kg) x V

40 kg m/s = 1.6kg x V

V = (40 kg m/s) / 1.6 kg

V = 25 m/s

Attempt at b) (I'm a little unsure of this question)

So I used this equation: f=(v-u)/t

F = ( 25 m/s - 400 m/s)/ 0.10 seconds

F = -3750N

Attempt at c) (the answer to this question is dependent on on b) being correct)

F=ma

a=F/m

acceleration of projectile =3750N / 0.1kg
acceleration of projectile = 37500m/s^2

Acceleration of target= 3750N/1.5kg
Acceleration of target= 2500m/s^2

I just know I've done something wrong. Can someone please help me?

 

[jbriggs444]

The Attempt at a Solution

Attempt at a)

(0.1kg x 400m/s) + (1.5kg x 0m/s) = (0.1kg + 1.5kg) x V

40 kg m/s = 1.6kg x V

V = (40 kg m/s) / 1.6 kg

V = 25 m/s

This looks fine. It is usually better to keep your equations in symbolic form while doing the algebra and only substitute numbers in at the end. It does not matter much when the equations are simple, but for more complex equations, you can more readily see simplifications. It's also usually less writing.

Attempt at b) (I'm a little unsure of this question)

So I used this equation: f=(v-u)/t

Where does the equation "f=(v-u)/t" come from? What are v and u? What are their units?

F = ( 25 m/s - 400 m/s)/ 0.10 seconds

If you divide meters per second by seconds, what would the units for the result be?

 

[NewtonIsAmazing]

This looks fine. It is usually better to keep your equations in symbolic form while doing the algebra and only substitute numbers in at the end. It does not matter much when the equations are simple, but for more complex equations, you can more readily see simplifications. It's also usually less writing.
Where does the equation "f=(v-u)/t" come from? What are v and u? What are their units?

I want to find the average force. V is the final velocity and U is the initial velocity. Their units are m/s

If you divide meters per second by seconds, what would the units for the result be?

Question c) is dependent on question b) being correct.

Is question b) correct? if not, what have I done wrong?

 

[stockzahn]

Attempt at a)

(0.1kg x 400m/s) + (1.5kg x 0m/s) = (0.1kg + 1.5kg) x V

40 kg m/s = 1.6kg x V

V = (40 kg m/s) / 1.6 kg

V = 25 m/s

This is correct.

Attempt at b) (I'm a little unsure of this question)

So I used this equation: f=(v-u)/t

F = ( 25 m/s - 400 m/s)/ 0.10 seconds

F = -3750N

Have another look at the units of your calculation of the force - you missed something.

Attempt at c) (the answer to this question is dependent on on b) being correct)

F=ma

a=F/m

acceleration of projectile =3750N / 0.1kg
acceleration of projectile = 37500m/s^2

Acceleration of target= 3750N/1.5kg
Acceleration of target= 2500m/s^2

I just know I've done something wrong. Can someone please help me?

The calculations are basically correct, but the values you gained in b) are wrong. Plus: There's an easier way to calculate the acceleration without using the results from b). What's the definition of acceleration in kinematics (not dynamics)?

 

[NewtonIsAmazing]

Have another look at the units of your calculation of the force - you missed something.

I'm not sure what I've missed

The calculations are basically correct, but the values you gained in b) are wrong. Plus: There's an easier way to calculate the acceleration without using the results from b). What's the definition of acceleration in kinematics (not dynamics)?

V = U + AT ?

 

[stockzahn]

I'm not sure what I've missed

Write down the units of your equation without the actual values.

V = U + AT ?

Try to solve for A, maybe you'll see the answer then.

 

[NewtonIsAmazing]

Write down the units of your equation without the actual values.

N = (m/s - m/s)/s

Those are the units

Try to solve for A, maybe you'll see the answer then.

a = (v - u)/t

a = (25 - 400)/0.1

a = - 2750 m/s^2 (for the projectile)

a = (25 - 0) / 0.1
a = 250m/s^2 (for the target)

is this correct?

 

[stockzahn]

N = (m/s - m/s)/s

Those are the units

Does that seem correct to you? N = m/s²

a = (v - u)/t

a = (25 - 400)/0.1

a = - 2750 m/s^2 (for the projectile)

a = (25 - 0) / 0.1
a = 250m/s^2 (for the target)

is this correct?

Except for a small mistake in the calculus for the projectile, yes.

 

[NewtonIsAmazing]

Does that seem correct to you? N = m/s²

So which values should I plug into N = m/s^2?

Except for a small mistake in the calculus for the projectile, yes.

What mistake did I make?

 

[stockzahn]

So which values should I plug into N = m/s^2?

What's the definition of 1 N (force)? 1 N = 1 ...

What mistake did I make?

(25 - 400) = ...

 

[NewtonIsAmazing]

What's the definition of 1 N (force)? 1 N = 1 ...

I'm not sure

(25 - 400) = ...

So should it be 400-25 instead?

 

[stockzahn]

I'm not sure

I'm sure you find that within 30 seconds on the internet, if you don't know it.

So should it be 400-25 instead?

No, the formula was correct, just the result was wrong.

 

[NewtonIsAmazing]

I'm sure you find that within 30 seconds on the internet, if you don't know it.

So 1N = 1 kg metres per second squared?

No, the formula was correct, just the result was wrong.

So what exactly did I get wrong in the working out?

 

[stockzahn]

So 1N = 1 kg metres per second squared?

Correct. Now try to use it for calculating b).

So what exactly did I get wrong in the working out?

(25-400) = -375, not -275

 

[NewtonIsAmazing]

Correct. Now try to use it for calculating b).

Which kilogram should I use? The kg for the projectile or the target?

 

[jbriggs444]

Which kilogram should I use? The kg for the projectile or the target?

Which mass you should use depends on which acceleration you calculated. Which acceleration did you calculate?

 

[stockzahn]

In your initial attempt you wanted to calculat the force with difference in movement of the projectile... If you continue with that you have to use the projectile's mass. But according to Newton's 3rd law you get the same result calculating the force with all data of the wood.

 

[NewtonIsAmazing]

In your initial attempt you wanted to calculat the force with difference in movement of the projectile... If you continue with that you have to use the projectile's mass. But according to Newton's 3rd law you get the same result calculating the force with all data of the wood.

F=0.1kg(25m/s-400m/s)/0.1s
F=-375N

Is this the correct answer for b)?

 

[stockzahn]

F=0.1kg(25m/s-400m/s)/0.1s
F=-375N

Is this the correct answer for b)?

Yes, that's it.