1. More Momentum Conservation of Momentum/Energy
Elastic and inelastic collisions
Physics 1D03 - Lecture 27

2. Example 1: The three air carts shown below have masses, reading from left to right, of m , 2m, and 4m respectively. Initially, the cart on right is at rest, whereas the other two carts are moving to the right with speed vo. All carts have putty bumpers that give completely inelastic collisions. The final speed of the carts are:
Physics 1D03 - Lecture 27

3. Example 2 – the ballistic pendulum: A bullet with velocity vb and mass m hits a stationary wooden block of mass M hanging on a string. Given that the block swings through a height h, determine the initial speed
of the bullet.
Physics 1D03 - Lecture 27

4. at McMaster, Tarzan (m=100kg) swings from a 5m long rope that
Example 3 –Tarzan: To save a student from falling into one of the construction holes
at McMaster, Tarzan (m=100kg) swings from a 5m long rope that
makes an angle of 60 degrees with the horizontal initially. If the
student with her physics books has a mass of 50kg, to what new
height will they swing together?
Physics 1D03 - Lecture 27

5. 4m/s on frictionless horizontal surface collides with a spring
Example 4: A block of mass m1=1.6kg initially moving right with a speed of
4m/s on frictionless horizontal surface collides with a spring
attached to a second block of mass m2=2.1kg initially moving
to the left at 2.5m/s. The spring constant is 600N/m.
Q: What type of a collision is this?
a) Find the velocities of the blocks after the collision. b) Determine the maximum compression of the spring.
Physics 1D03 - Lecture 27

6. Solution
Physics 1D03 - Lecture 27

7. Quiz
An object of mass 3m, initially at rest, explodes breaking into two fragments of mass m and 2m respectively. Which one of the following statements concerning the fragments after the explosion is true?
They may fly off at right angles.
The may fly off in the same direction.
The smaller fragment will have twice the speed of the larger fragment.
The larger fragment will have twice the speed of the smaler fragment.
The smaller fragment will have four times the speed of the larger fragment
Physics 1D03 - Lecture 27

8. Quiz: The figure below shows four identical blocks on a frictionless floor.
Initially blocks a and b are moving rightward and block c and d are
moving leftward, each with speed v. A series of elastic collisions
occurs. After the last collision, the speeds and directions of motions
of each blocks are:
A) a and b move leftward with v/2, and c and d rightward with v/2.
B) a and b move leftward with v, and c and d rightward with v.
C) b and c at rest and a leftward with v and d rightward with v.
D) b and c at rest and a leftward with 2v and d rightward with 2v.
E) they all have v=0 after the collisions
Physics 1D03 - Lecture 27

9. Example: Rockets thrust
How can we calculate the thrust on a rocket when gas of mass Dm is ejected out of the nozzle in time Dt ?
If we take the external force to be zero to simplify (-mg actually), then we have:
gas
thrust
Thrust = (speed of gas relative to nozzle)x(mass of gas ejected per unit time). Note, dm/dt < 0 so T>0.
Physics 1D03 - Lecture 27

10. Example: Limits on rocket speed… This is further reduced by gravity, and air resistance!
Physics 1D03 - Lecture 27