Impulse (J) J = FΔ t Momentum Δp = mδv Impulse and Momentum j = (F)( p = ( )(v) F)(Δ ) = ( )(Δv)

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1 Impulse (J) We create an unbalancing force to overcome the inertia of the object. the integral of force over time The unbalancing force is made up of the force we need to unbalance the object and the time that we use this force and is called Impulse (j). J = FΔ t F = force in Newtons Δt = time interval in seconds Momentum The rate of change of momentum is equal to the net force applied to it. Since Force is a vector, it follows that momentum (p) is also a vector. Δp = mδv m = mass in kg Δv = change in velocity Momentum and Impulse may be expressed in kgm/s or in Ns. Impulse and Momentum Impulse produces motion. j = (F)(t) Momentum is the mass (m) sent to a certain speed (v) p = (m)(v) The impulse used and the momentum change are equal so (F)(Δt) = (m)(δv) Impulse and momentum are VECTORS

2 Problem 1 An engine of the orbital maneuvering system (OMS) on a space shuttle exerts a force of N for 4.00 s, exhausting a negligible mass of fuel relative to the 95,000 kg mass of the shuttle. (a) What is the impulse of the force for this 4.00 s? (b) What is the shuttle's change in momentum from this impulse? (c) What is the shuttle's change in velocity from this impulse? (d) Why can't we find the resulting change in kinetic energy of the shuttle? Problem 2 A particle with momentum mv 1 experiences a force which leaves it with momentum mv 2. Draw an arrow to represent the impulse the particle experienced. Problem 3 A 1000 kg car accidentally drops from a crane and crashes at 30 m/s to the ground below and comes to an abrupt halt. What impulse acts on the car when it crashes?

3 Problem 4 A billiard ball approaches a cushioned edge of a billiard table with momentum, p. After the collision with the cushion, it bounces straight back with the same amount of momentum in the opposite direction. What is the impulse on the ball? Problem 5 A bullet, of mass 20 g, traveling at 350 m/s, strikes a steel plate at an angle of 30- degrees with a plane of the plate. It ricochets off at the same angle, at a speed of 320 m/s. What is the magnitude of the impulse that the wall gives to the bullet? Problem 6 A bungee jumper (m = kg) tied to a m cord, leaps off a m tall bridge. He falls to 9.00 m above the water before the bungee cord pulls him back up. What size impulse is exerted on the bungee jumper while the cord stretches.

4 Problem 7 While waiting in his car at a stoplight, an 80-kg man and his car are suddenly accelerated to a speed of 5 m/s as a result of a rear-end collision. Assuming the time taken to be 0.3s, find the a) impulse on the man and b) the average force exerted on him by the back seat of his car Impulse Problem A 53-g ball is dropped from a height of 2 m then bounces to a height of 1.7 m. What was the change in momentum of the ball? What was the outside impulse acting on the ball? What happened to the kinetic energy of the ball? Conservation of Momentum In CLOSED SYSTEMS where mass is not gained or lost AND in ISOLATED SYSTEMS where no forces are acting external to the system momentum is conserved. That means the TOTAL momentum you start with is equal to the TOTAL momentum you end with.

5 Elastic Collisions No Energy Loss! p total initial = p total final p black initial + p gray initial = p black final + p gray final m black v black initial + m gray v gray initial = m black v black final + m gray v gray final Inelastic Collisions Loss of Kinetic Energy p total initial = p total final p black initial + p gray initial = p black final + p gray final m black v black initial + m gray v gray initial = (m black + m gray )v final Explosions Energy Added Explosions are inelastic collisions in reverse Conversion of Internal Energy to Kinetic Energy p total initial = p total final p total initial = p 1st final + p 2nd final m total v initial = m 1st v 1st final + m 2nd v 2nd final

6 Proofs and Examples one/lessonch/06moment/momvect/sld001. htm Proof Conservation of Energy In elastic collisions both momentum and kinetic energy are conserved. Therefore: p 1 = p 2 and KE 1 = KE 2 Show that this allows you to determine that: (v a + v a ) = (v b + v b )

7 Elastic Collision A 4.0 kg ball with a velocity of 4.0 m/s in the +x direction elastically collides headon with a stationary 2.0 kg ball. What are the velocities of the balls after the collision? 2-D Collisions Just like displacement velocity, acceleration, and force, Impulse and Momentum are vector quantities. That means that collisions at an angle must be solved by breaking the problem into component vectors. Example 1 A two balls are rolling across a frictionless surface. The smaller ball is 0.25 kg; the larger is 1 kg. The large ball moves at 5 m/s, the small at 10 m/s. If the balls move as shown after the collision, solve for the final velocity of both.

8 Problem 1 In playing a game of pool, you line the cue ball up with a second ball. You know the initial speed of the cue ball to be about 20 cm/s and the other ball is stationary. You also know that the mass of the cue ball is about 0.17 kg and the mass of the other balls to be about 0.15 kg. How fast will both balls be traveling after a headon collision? Problem 2 In pool, many of the collisions are glancing collisions. These are more realistic collisions that involve a ball striking another ball and then either one or the other moving at an angle to the horizontal. Let s say that one ball strikes another stationary ball of the same mass at 40 cm/s. The final velocity of the initially moving billiard is 35 cm/s at an angle of 25 degrees to the horizontal. What is the final velocity and angle to the horizontal of the second ball after the collision? Inelastic Collisions & Explosions Inelastic collisions occur when the two objects stick together afterward (Kinetic energy changed to Thermal energy) Explosions occur when a single object is separated into multiple objects by the explosive release of some internal energy.

9 Sample Problem A hollow wooden block is cut into two pieces, one with three times the mass as the other. A firecracker is placed inside the block and the pieces are reassembled. When the firecracker explodes, the two pieces separate and slide apart across a surface with friction. What is the ratio of distances traveled by the two pieces? A block of mass M is resting on a horizontal, frictionless table and is attached as shown above to a relaxed spring of spring constant k. A second block of mass 2M and initial speed v 0 collides with and sticks to the first block. Develop expressions for the following quantities in terms of M, k, and v 0. v, the speed of the blocks immediately after impact x, the maximum distance the spring is compressed A massless spring is between a 1-kilogram mass and a 3-kilogram mass as shown above, but is not attached to either mass. Both masses are on a horizontal frictionless table. In an experiment, the 1-kilogram mass is held in place, and the spring is compressed by pushing on the 3-kilogram mass. The 3-kilogram mass is then released and moves off with a speed of 10 meters per second. Determine the minimum work needed to compress the spring in this experiment. The spring is compressed again exactly as above, but this time both masses are released simultaneously. Determine the final velocity of each mass relative to the table after the masses are released.

10 Ballistic Pendulum Problem ON YOUR OWN QUIETLY Complete the ballistic pendulum problem. Due at the end of class.