Ch 09: Momentum & ImpulseWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Intro to Collisions with Motion

Practice: A 40-kg crate is released from rest from the top of a 10-m long, smooth inclined plane that makes an angle of 53° with the horizontal. At the bottom of the plane, a 50-kg crate is initially at rest on a smooth horizontal surface. After hitting the second crate, the first crate stands still. Calculate the speed of the second crate after the collision.

Concept #2: Collisions & Motion: Finding Initial Velocity

Example #1: Collisions with Pendulums

Example #2: Collisions with Pendulums

Additional Problems
A bullet of mass 24 g is fired into the bob of a ballistic pendulum of mass 2.85 kg. When the bob is at its maximum height, the strings make an angle of 40° with the vertical. The length of the pendulum is 3.75 m. Find the speed of the bullet (in units of m/s). The acceleration due to gravity is 9.81 m/s2 . 
Block A with mass 0.050 kg is released from rest at the rim of a frictionless hemispherical bowl that has radius R = 0.600 m. Block A slides down the side of the bowl and strikes block B, which has mass 0.150 kg and that is sitting at rest at the bottom of the bowl, and the two blocks stick together. What maximum vertical distance above the bottom of the bowl will the combined object reach after the collision?  
A bullet with mass 6.00 x 10-3 kg is fired horizontally with speed V0 into a 1.20 kg wood block that is initially at rest on a horizontal surface. The coefficient of kinetic friction between the block and the surface is 0.200, The bullet remains embedded in the block and after the collision with the bullet the block slides 0.120 m before coming to rest. What was the initial speed V0 of the bullet?
A 3.0 kg block moving at 12.0 m/s along a horizontal frictionless surface collides with a 2.0 kg block that is initially at rest. After the collision, the two blocks stick together and then slide up a 53° frictionless inclined plane, as shown in the sketch. Calculate the maximum distance L that the two blocks travel up the incline.
A block with mass 4.95 kg is on a horizontal frictionless surface. It rest against a horizontal spring that has force constant k = 300 N/m. Initially the spring is not compressed. A bullet with mass 0.0500 kg is travelling horizontally with speed v0 = 400 m/s. The bullet strikes the block and remains embedded in it. What is the maximum distance that the spring is compressed after the collision with the bullet?
A truck is stopped at a stop light on a street in San Francisco with an 18% grade (a 10° incline), facing down the incline. A distracted driver driving a sedan down the same road does not notice the red light, nor the truck, and collides with the back of the truck at full speed. The car and truck stick together after the collision and slide to a stop down the road. The police investigating the accident want to know if the car was going above the speed limit, set at 25 miles per hour. The police determine that the car and truck slid a distance of 4 m together after the collision. Determine if the car was speeding before it collided with the truck. A typical mass for a sedan is 1400 kg, while a truck has a mass of 2000 kg. The coefficient of kinetic friction between car tires and dry pavement is 0.6.
The ballistic pendulum is a system used to measure the speed of a fast-moving projectile, such as a bullet. The bullet is fired into a large block of wood suspended from some light wires. The bullet embeds in the block, and the entire system swings through a height h since the collision is perfectly inelastic. Suppose that h = 5.0 cm, m1 = 0.5 g, and m2 = 1 kg. Find the initial speed of the bullet.
A test car of mass 740 kg is moving at a speed of 7.3 m/s when it crashes into a wall to test its bumper. If the car comes to rest in 0.36 s, how much average power is expended in the process? 1. 42820.9 2. 47940.6 3. 59118.6 4. 49662.2 5. 50789.2 6. 54770.3 7. 45825.2 8. 44990.3 9. 46540.4 10. 51904.1
A 13.9 g bullet is fired horizontally into a 0.518 kg wooden block resting on a horizontal surface (μ = 0.125). The bullet goes through the block and comes out with a speed of 233 m/s. If the block travels 7.29 m before coming to rest, what was the initial speed of the bullet? The acceleration of gravity is 9.8 m/s2. 1. 421.185 2. 462.083 3. 475.131 4. 428.393 5. 771.008 6. 608.548 7. 390.493 8. 415.722 9. 506.991 10. 636.296
In the figure, a block sitting on a frictionless horizontal surface is attached to a rigid wall on the right through a spring (whose axis is horizontal). A bullet is shot at the block from the left and gets embedded in it, causing the block to move to the right, thus compressing the spring. (Assume the bullet is travelling perfectly horizontally, along the axis of the spring, before hitting the block). Which of the following are true? A. The initial kinetic energy of the bullet is completely converted to spring potential energy when the spring reaches its maximal compression. B. The initial momentum of the bullet is equal to the momentum of the bullet+block system just after the bullet enters the block. C. Part of the momentum of the bullet+block system is lost during the collision (i.e. before the spring-compression starts). D. Part of the energy of the bullet+block system is ”lost” (no longer present as macroscopic kinetic energy) during the collision, before the spring-compression starts. E. If we are given the masses of the block and the bullet, the initial speed of the bullet and the spring constant, it is possible to find the maximum compression of the spring. 1. A, E 2. A, B, D 3. B, D 4. A, B 5. A, C 6. D 7. B, D, E 8. A, C, E 9. A, B, E
If all three collisions in the figure are totally inelastic, which cause(s) the most damage (deformation of objects, thermal energy increase, etc.)? Assume that the wall is stationary and the car is completely stopped by it in the first diagram. 1. I, III 2. I 3. all three 4. I, II 5. II, III 6. III 7. II