This is Example Problem #1.
Problem #1 is just like part a) below.

1.) A 325 kg motorcycle is moving at 140 km/h, south.
     a) Find its momentum.
     b) At what velocity is the momentum of a 1754 kg car equal to that of the motorcycle?













































This is Example Problem #1.
Problem #2 is very similar.

1.) A 325 kg motorcycle is moving at 140 km/h, south.
     a) Find its momentum.
     b) At what velocity is the momentum of a 1754 kg car equal to that of the motorcycle?













































This is Example Problem #1.
Problem #3 is very similar to part a) except you must solve for "m".

1.) A 325 kg motorcycle is moving at 140 km/h, south.
     a) Find its momentum.
     b) At what velocity is the momentum of a 1754 kg car equal to that of the motorcycle?













































This is Example Problem #2.
Problem #4 is very similar.

2.) Initially a soccer ball is going 23.5 m/s, south. In the end, it is traveling at 3.8 m/s, south.
     The ball's change in momentum is 17.24 kg m/s, north. Find the ball's mass.













































This is Example Problem #2.
Problem #5 is very similar except you don't
need to rearrange the formula: Δ ρ = m ( vf - vi ).

2.) Initially a soccer ball is going 23.5 m/s, south. In the end, it is traveling at 3.8 m/s, south.
     The ball's change in momentum is 17.24 kg m/s, north. Find the ball's mass.













































This is Example Problem #2.
Problem #6 is very similar except you
need to rearrange the formula: Δ ρ = m ( vf - vi ) .
It becomes for vi = [ Δ ρ - m vf] / m

2.) Initially a soccer ball is going 23.5 m/s, south. In the end, it is traveling at 3.8 m/s, south.
     The ball's change in momentum is 17.24 kg m/s, north. Find the ball's mass.













































This is Example Problem #3.
Problem #7 uses the derived formula: Δ ρ = FNet t
shown in part b) below. Use it to calculate Δ ρ .

3.) A bobsled has a mass of 1.357 x 102 kg. A constant force is exerted on it for 5.42 s.
     The sled's initial velocity is zero and its final velocity is 8.73 m/s, east.
     a) What is its change in momentum?
     b) What is the net force exerted on it?













































This is Example Problem #3.
Problem #8 is very similar.

3.) A bobsled has a mass of 1.357 x 102 kg. A constant force is exerted on it for 5.42 s.
     The sled's initial velocity is zero and its final velocity is 8.73 m/s, east.
     a) What is its change in momentum?
     b) What is the net force exerted on it?













































In Problem #9, combine:

Δ ρ = m ( vf - vi ) and Δ ρ = FNet t

by setting Δ ρ = Δ ρ.

You will get: m ( vf - vi ) = FNet t

Then solve for: t


From previous work, we know that weight = Fg = mg and therefore m = Fg / g.













































In Problem #10, combine:

Δ ρ = m ( Δ v ) and Δ ρ = FNet t

by setting Δ ρ = Δ ρ.

You will get: m ( Δ v ) = FNet t

Then solve for: t













































This is Example Problem #4.
Problem #11 is very similar except
both vB and v'A are equal to zero.

4.) A 62.0 kg curler travelling at + 1.72 m/s runs into a 78.1 kg curler and the 62.0 kg curler
     comes to a stop. If the 78.1 kg curler was originally moving at + 0.85 m/s, find his velocity
     after the interaction.













































This is Example Problem #4.
Problem #12 is very similar.

4.) A 62.0 kg curler travelling at + 1.72 m/s runs into a 78.1 kg curler and the 62.0 kg curler
     comes to a stop. If the 78.1 kg curler was originally moving at + 0.85 m/s, find his velocity
     after the interaction.













































This is Example Problem #4.
Problem #13 is very similar except
instead of v'A = 0, this time vB = 0.

4.) A 62.0 kg curler travelling at + 1.72 m/s runs into a 78.1 kg curler and the 62.0 kg curler
     comes to a stop. If the 78.1 kg curler was originally moving at + 0.85 m/s, find his velocity
     after the interaction.













































Problem #14 is very similar to Problem #13 except
instead of v'A being in the same direction as vA,
this time it is in the opposite.













































Problem #15 is very similar to Problem #13 & 14
except this time NONE of the velocities are zero.

(Be careful with the signs on each of the velocities.)













































This is Example Problem #5.
Problem #16 is very similar.

5.) A 62.0 kg curler runs into a stationary 78.1 kg curler and they hold on to each other.
     Together they move away at 1.29 m/s, west. What was the original velocity of the 62.0 kg curler?













































This is Example Problem #5.
Problem #17 is very similar.

5.) A 62.0 kg curler runs into a stationary 78.1 kg curler and they hold on to each other.
     Together they move away at 1.29 m/s, west. What was the original velocity of the 62.0 kg curler?













































This is Example Problem #6.
Problem #18 is very similar.

6.) A 84.0 kg (total mass) astronaut in space fires a thruster that expels 35 g
     of hot gas at 875 m/s. What is the velocity of the astronaut after firing the shot?













































This is Example Problem #6.
Problem #19 is very similar.

6.) A 84.0 kg (total mass) astronaut in space fires a thruster that expels 35 g
     of hot gas at 875 m/s. What is the velocity of the astronaut after firing the shot?













































This is Example Problem #6.
Problem #20 is very similar except
vA & vB ≠ 0, instead vA = vB = 5.0 m/s and v'B = 0.

6.) A 84.0 kg (total mass) astronaut in space fires a thruster that expels 35 g
     of hot gas at 875 m/s. What is the velocity of the astronaut after firing the shot?













































This is Example Problem #6.
Problem #21 is very similar.
vA = vB = 0

6.) A 84.0 kg (total mass) astronaut in space fires a thruster that expels 35 g
     of hot gas at 875 m/s. What is the velocity of the astronaut after firing the shot?













































Problem #22 is very tricky!

Given only:

Δ dxball = 215 m
mcannon = 4.5 kg
mcannon = 225 kg

It doesn't seem like enough information!















































Below is Example Problem #7.
Problems #23, 24, 25, 26 are very similar.
There is a
solution for #25.

In each case, you must analyze in both the x and y directions.
Determine which velocities = 0 to simplify the equations.

The magnitude of the resultant velocity, in each case,
will be found using the Pythagoreon Theorem.
The resultant angle will require Trig. [ θ = Tan-1 (y / x) ]

7.) A 80.0 kg scrum-half moving south at 5.75 m/s runs into a stationary 97.0 kg full-back. The
    scrum-half moves away at 4.62 m/s, 250o. Find the velocity of the full-back after the interaction.




Does this result make sense?

Click on drawing below.



Click here.













































Does this result make sense?

solutions/example 7.jpgClick here.

Put Momentum vectors tip to tail to Add.
Click on second drawing.













































Does this result make sense?

Yes, it does. The Total momentum before equals the Total momentum after.













































25.) A 1325 kg car moving north at 27.0 m/s collides with a 2165 kg car moving east at 17.0 m/s.
       They stick together. What is their velocity after the collision?