# Physics Dynamics Q (1 Viewer)

help

#### Drdusk

##### π
Moderator
I gotcha

Split the question up into 3 parts. Part 1: The dart is going through the tube. Part 2: The dart is moving and collides with the block. Part 3: The dart and block system move together

For part 1:
Recall the formula of Work done and write it out for this question which is trivial:

$\bg_white FL = \dfrac{1}{2}mv^2$

Part 2:
For this part remember it is an inelastic collision between the dart and the block which means momentum is conserved but energy isn't. Using this you can find out an expression for the start/initial velocity of the dart & block system as it begins to move.

Part3:
Now for this part you get an expression for the friction force being:

$\bg_white F_f = \mu_k N = -(m+M)\mu_k g$

Now again recall the formula for Work done and find an expression for D in terms of m,v,u_k and g.

Finally take a look at part 1 again and substitute appropriately into the expression you obtain in part 3 for D and that gives you the final answer!

#### idkkdi

##### Well-Known Member
I gotcha

Split the question up into 3 parts. Part 1: The dart is going through the tube. Part 2: The dart is moving and collides with the block. Part 3: The dart and block system move together

For part 1:
Recall the formula of Work done and write it out for this question which is trivial:

$\bg_white FL = \dfrac{1}{2}mv^2$

Part 2:
For this part remember it is an inelastic collision between the dart and the block which means momentum is conserved but energy isn't. Using this you can find out an expression for the start/initial velocity of the dart & block system as it begins to move.

Part3:
Now for this part you get an expression for the friction force being:

$\bg_white F_f = \mu_k N = -(m+M)\mu_k g$

Now again recall the formula for Work done and find an expression for D in terms of m,v,u_k and g.

Finally take a look at part 1 again and substitute appropriately into the expression you obtain in part 3 for D and that gives you the final answer!
Ye, just realised I was trying to get v2 via energy formulas, but energy isn't conserved so gotta switch to momentum.

#### Drdusk

##### π
Moderator
Ye, just realised I was trying to get v2 via energy formulas, but energy isn't conserved so gotta switch to momentum.
Yeah be careful mate! Make sure you know when you can use each one.