Impulse Momentum, and Collisions

1. Impulse Momentum, and Collisions Take Home Test

2. What type of collision is this? Take Home Test An 8.00 g bullet is fired into a 250 g block that is initially at rest at the edge of a table of height 1.00 m. The bullet remains in the block, and after the impact the block lands 2.00 m from the bottom of the table. Determine the initial speed of the bullet. Perfectly Inelastic Collision We must first figure out the combined Vf, how can we do that? Knows m1= .008 kg m2 = 0.250kg V2i = 0 V1f = V2f h=Δy =1.00m Δx = 2.00m Unknowns V1i = ? V1f = V2f = ? What else about this situation do we know? What else about this situation don’t we know? But wait! There’s more Can we figure out time, then Vf? Now what? Vix = Vf, because velocity is Constant in the x-axis, no accel. In the X. Projectile

3. What type of collision is this? Take Home Test An 8.00 g bullet is fired into a 250 g block that is initially at rest at the edge of a table of height 1.00 m. The bullet remains in the block, and after the impact the block lands 2.00 m from the bottom of the table. Determine the initial speed of the bullet. Perfectly Inelastic Collision Knows m1= .008 kg m2 = 0.250kg V2i = 0 V1f = V2f h=Δy =1.00m Δx = 2.00m Unknowns V1i = ? V1f = V2f = ?

4. What type of collision is this? Take Home Test • A 1200 kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9000 kg truck moving in the same direction at 20.0 m/s. The velocity of the car right after the collision is 18.0 m/s to the east. What is the velocity of the truck right after the collision? How much mechanical energy is lost in the collision? Account for this loss in energy. Elastic Collision

5. What type of collision is this? Take Home Test A 1200 kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9000 kg truck moving in the same direction at 20.0 m/s. The velocity of the car right after the collision is 18.0 m/s to the east. What is the velocity of the truck right after the collision? How much mechanical energy is lost in the collision? Account for this loss in energy. Elastic Collision

6. Take Home Test A block of mass m1 = 1.60 kg, initially moving to the right with a velocity of 4.00 m/s on a frictionless horizontal track, collides with a massless spring attached to a second block of mass m2 = 2.10 kg moving to the left with a velocity of -2.50 m/s. The spring has a spring constant of 6.00 X 102 N/m. Determine the velocity of block 2 at the instant when block 1 is moving to the right with a velocity of +3.00 m/s. Find the compression of the spring. Elastic Collision Now we have solved for a). What is the next step to solving for the compression of the spring xf? Conservation of Momentum Since there is no friction, hence no loss of energy how could we simplify this? Conservation of Energy ->

7. Take Home Test A block of mass m1 = 1.60 kg, initially moving to the right with a velocity of 4.00 m/s on a frictionless horizontal track, collides with a massless spring attached to a second block of mass m2 = 2.10 kg moving to the left with a velocity of -2.50 m/s. The spring has a spring constant of 6.00 X 102 N/m. Find the compression of the spring. Conservation of Xi = 0, now solve for Xf Distribute the 2 canceling all ½ Divide out k and √ both sides

8. What type of collision? Take Home Test • A car with mass 1.50 x 103 kg traveling east at a speed of 25.0 m/s collides at an intersection with a 2.50 x 103 kg van traveling north at a speed of 20.0 m/s. Find the magnitude and direction of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision (that is, they stick together) and assuming that frictions between the vehicles and the road can be neglected. Conservation of momentum, Expand this equation out for perfectly inelastic collision The pf is moving in two dimension of space, oh no! The combined velocities are 2D pxf pyf Δp, but we don’t know the θ What do we know? We know what cosθ is We know what sinθ is The definition of tangent is the ratio of sinθ to cosθ

9. What type of collision? Take Home Test • A car with mass 1.50 x 103 kg traveling east at a speed of 25.0 m/s collides at an intersection with a 2.50 x 103 kg van traveling north at a speed of 20.0 m/s. Find the magnitude and direction of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision (that is, they stick together) and assuming that frictions between the vehicles and the road can be neglected. Conservation of momentum, Expand this equation out for perfectly inelastic collision The pf is moving in two dimension of space, oh no! The combined velocities are 2D pxf pyf Δp, but we don’t know the θ What do we know? We know what cosθ is We know what sinθ is The definition of tangent is the ratio of sinθ to cosθ

10. What type of collision? Take Home Test A car with mass 1.50 x 103 kg traveling east at a speed of 25.0 m/s collides at an intersection with a 2.50 x 103 kg van traveling north at a speed of 20.0 m/s. Find the magnitude and direction of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision (that is, they stick together) and assuming that frictions between the vehicles and the road can be neglected. The definition of tangent is the ratio of sinθ to cosθ What can I do with this information? Do I know what cosθ is equal to? Do I know what sinθ is equal to? What can I do with this information?

11. Take Home Test Consider a frictionless track. A block of mass m1 = 5.00 kg is released from A. It makes a head-on elastic collision at B with block of mass m2 = 10.0 kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision m2 moves to the right with a velocity of 3.3 m/s.

12. The End