MOMENTUM Momentum Momentum can be defined as mass

MOMENTUM

Momentum � Ø Ø � � Momentum can be defined as "mass in motion. " All objects have mass; so if an object is moving, then it has momentum Momentum depends upon the variables mass and velocity. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object. Momentum (p) = mass • velocity momentum is directly proportional to an object's mass and directly proportional to the object's velocity.

� � � Momentum is a vector quantity The direction of the momentum vector is the same as the direction of the velocity of the object https: //www. youtube. com/watch? v=y 2 Gb 4 NIv 0 Xg

Question Determine the momentum of a. . . a. 60 -kg halfback moving eastward at 9 m/s. b. 1000 -kg car moving northward at 20 m/s. c. 40 -kg freshman moving southward at 2 m/s. �

Answer A. p = m*v = 60 kg*9 m/s p = 540 kg • m/s, east � B. p = m*v = 1000 kg*20 m/s p = 20 000 kg • m/s, north � C. p = m*v = 40 kg*2 m/s p = 80 kg • m/s, south �

Question A car possesses 20 000 units of momentum. What would be the car's new momentum if. . . a. its velocity was doubled. b. its velocity was tripled. c. its mass was doubled (by adding more passengers and a greater load) d. both its velocity was doubled and its mass was doubled. �

Answer � � A. p = 40 000 units (doubling the velocity will double the momentum) B. p = 60 000 units (tripling the velocity will triple the momentum) C. p = 40 000 units (doubling the mass will double the momentum) D. p = 80 000 units (doubling the velocity will double the momentum and doubling the mass will also double the momentum; the combined result is that the momentum is doubled twice quadrupled)

� � � The more momentum that an object has, the harder that it is to stop. To stop an object, it is necessary to apply a force against its motion for a given period of time. As the force acts upon an object for a given amount of time, the object's velocity is changed; and therefore, the object's momentum is changed.

� Ø Ø an unbalanced force always accelerates an object - either speeding it up or slowing it down If the force acts opposite the object's motion, it slows the object down. If a force acts in the same direction as the object's motion, then the force speeds the object up. Either way, a force will change the velocity of an object. And if the velocity of the object is changed, then the momentum of the object is changed.

� � � F = m • a (Newton’s second law) F = m • ∆v / t If both sides of the above equation are multiplied by the quantity t, a new equation results. F • t = m • ∆v

Impulse � Ø � � F • t = m • ∆v the force times the time equals the mass times the change in velocity. the quantity Force • time is known as impulse Impulse = Change in momentum

� � In a collision, an object experiences a force for a specific amount of time that results in a change in momentum. The result of the force acting for the given amount of time is that the object's mass either speeds up or slows down (or changes direction). The impulse experienced by the object equals the change in momentum of the object. In equation form, F • t = m • Δ v. In a collision, the impulse experienced by an object is always equal to the momentum change.

Question � Vector Diagram � Greatest velocity change? Greatest acceleration? Greatest momentum change? Greatest Impulse? � � �

Answer � � a. The velocity change is greatest in case B. The velocity changes from +30 m/s to -28 m/s. This is a change of 58 m/s (-) and is greater than in case A ( -15 m/s). b. The acceleration is greatest in case B. Acceleration depends on velocity change and the velocity change is greatest in case B (as stated above) c. The momentum change is greatest in case B. Momentum change depends on velocity change and the velocity change is greatest in case B (as stated above). d. The impulse is greatest in case B. Impulse equals momentum change and the momentum change is greatest in case B (as stated above).

Question � Velocity-Time Graph � Greatest velocity change? Greatest acceleration? Greatest momentum change? Greatest Impulse? � � �

Answer � � a. The velocity change is greatest in case A. The v changes from +5 m/s to -3 m/s. This is a change of 8 m/s (-) and is greater than in case B (-4 m/s). b. The acceleration is greatest in case A. Acceleration depends on velocity change and the velocity change is greatest in case A (as stated above). c. The momentum change is greatest in case A. Momentum change depends on velocity change and the velocity change is greatest in case A (as stated above). d. The impulse is greatest in case A. Impulse equals momentum change and the momentum change is greatest in case A (as stated above).

Question � Ticker Tape Diagram � Greatest velocity change? Greatest acceleration? Greatest momentum change? � �

Answer � � a. The velocity change is greatest in case B. In each case the initial velocity is the same. In case B, the object rebounds in the opposite direction with a greater speed than in case A. This is equivalent to a change from +10 m/s to -5 m/s; whereas, case A has a change from +10 m/s to -2 m/s. b. The acceleration is greatest in case B. Acceleration depends on velocity change and the velocity change is greatest in case B (as stated above) c. The momentum change is greatest in case B. Momentum change depends on velocity change and the velocity change is greatest in case B (as stated above). d. The impulse is greatest in case B. Impulse equals momentum change and the momentum change is greatest in case B (as stated above)

impulse-momentum change theorem � � force and time are inversely proportional; for the same mass and velocity change, a tenfold increase in the time of impact corresponds to a tenfold decrease in the force of impact mass and force are directly proportional; for the same time and velocity change, a fivefold increase in the mass corresponds to a fivefold increase in the force required to stop that mass

impulse-momentum change theorem � � https: //www. youtube. com/watch? v=r 8 E 5 d. Un. Lm h 4 https: //www. youtube. com/watch? v=y. Upi. V 2 I_IRI

Question � A 5 kg object has a velocity of 8 m/s due east. An unbalanced force acts on the object for 3 s causing it to decrease to 2 m/s due east. Determine the magnitude and direction of the unbalanced force.

Answer J=∆P Ft=m∆V F=-10 kg*m/s 2 or -10 N and direction is to the west

COLLISIONS

� � Newton's third law : for every action there is an equal and opposite reaction In a collision between two objects, both objects experience forces that are equal in magnitude and opposite in direction. Such forces often cause one object to speed up (gain momentum) and the other object to slow down (lose momentum). The magnitude of the force is equal but the acceleration of an object is dependent upon both force and mass so, if the colliding objects have unequal mass, they will have unequal accelerations as a result of the contact force that results during the collision.

� Consider the collision between a moving seven ball and an eight ball that is at rest in the sport of table pool. When the seven ball collides with the eight ball, each ball experiences an equal force directed in opposite directions. The rightward moving seven ball experiences a leftward force that causes it to slow down; the eight ball experiences a rightward force that causes it to speed up. Since the two balls have equal masses, they will also experience equal accelerations. In a collision, there is a force on both objects that causes an acceleration of both objects; the forces are equal in magnitude and opposite in direction. For collisions between equal-mass objects, each object experiences the same acceleration.

Law of Momentum Conservation � � � For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision the momentum lost by object 1 is equal to the momentum gained by object 2 The Force is equal and opposite and the time is the same therefore the impulse is equal but opposite and therefore momentum is equal but opposite

Conservation of Momentum � � � A collision in a closed system, the change in momentum for each mass has the same magnitude but opposite direction. Law of conservation of momentum: the total momentum of the objects in a closed system is constant. Pbefore = Pafter

Question A large truck and a Volkswagen have a headon collision. a. Which vehicle experiences the greatest force of impact? b. Which vehicle experiences the greatest impulse? c. Which vehicle experiences the greatest momentum change? d. Which vehicle experiences the greatest acceleration? �

Answer � � � a, b, c: the same for each. Both the Volkswagon and the large truck encounter the same force, the same impulse, and the same momentum change d: Acceleration is greatest for the Volkswagon. While the two vehicles experience the same force, the acceleration is greatest for the Volkswagon due to its smaller mass.

Question � A 3000 -kg truck moving with a velocity of 10 m/s hits a 1000 -kg parked car. The impact causes the 1000 -kg car to be set in motion at 15 m/s. Assuming that momentum is conserved during the collision, determine the velocity of the truck immediately after the collision.

Answer Before Collision Truck 3000 • 10 = 30 000 Car 0 000 Total 30 000 3000*v + 15 000 = 30 000 3000*v = 15 000 v = 5. 0 m/s After Collision 3000 • v 1000 • 15 = 15 30 000

Question � A 0. 150 -kg baseball moving at a speed of 45. 0 m/s crosses the plate and strikes the 0. 250 -kg catcher's mitt (originally at rest). The catcher's mitt immediately recoils backwards (at the same speed as the ball) before the catcher applies an external force to stop its momentum. If the catcher's hand is in a relaxed state at the time of the collision, it can be assumed that no net external force exists and the law of momentum conservation applies to the baseball-catcher's mitt collision. Determine the post-collision velocity of the mitt and ball.

Answer � 0. 15 kg • v + 0. 25 kg • v = 6. 75 kg • m/s � � 0. 40 kg • v = 6. 75 kg • m/s � � v = 16. 9 m/s

Question � A 1 kg cart A is initially at rest on a frictionless air track. A. 20 kg cart B is moving to the right at 10 m/s. Cart B collides with cart A causing cart A to move to the right at 3 m/s. Determine the velocity of cart B after the collision.

Answer � � P after = P before VBf = -5 m/s