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

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

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

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

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

Solution Physics 1D03 - Lecture 27

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

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

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

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