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Chapter 6: Momentum and Impulse WEST VIRGINIA UNIVERSITY Physics Impulse Changing an object’s momentum requires the continuous application of a force during a time interval Δt: Definition of Impulse: unit: kg · m/s F m vi m vf Impulse is the change of an object’s momentum WEST VIRGINIA UNIVERSITY Physics Example problem: Car crash In a crash test, a car of mass 1500 kg collides with a wall and rebounds as shown in the figure. The initial and final velocities of the car are vi = -15 m/s and vf = 2.6 m/s, respectively. If the collision lasts for 0.15 s, find A. the impulse delivered to the car due to the collision. B. the size and direction of the average force exerted on the car. WEST VIRGINIA UNIVERSITY Physics The Physics of Injuries Let’s do an experiment (2 parts): 1. Take your fist and hit the table in front of you. Don’t hit too hard! → That hurts! 2. Now look at your neighbor…. Hit him/her against the arm. Move your fist at roughly the same speed as before. → That does not hurt so much! Why not? WEST VIRGINIA UNIVERSITY Physics The Physics of Injuries The change in momentum, i.e. the impulse, is the same in both experiments, since the initial velocity of your fist (before the collision) was the same and the final velocity was the same (vf = 0 m/s) in both experiment. The difference was the surface material your fist crashed into: Hard table top vs. soft arm! In case of the soft material (arm) your fist had more time to slow down. If the impulse is the same in both experiments, the force acting on your fist will be smaller, if the material is soft, since Δt is larger. This is the reason, why boxers wear boxing gloves and airbags are used in cars - to prevent serious injuries! WEST VIRGINIA UNIVERSITY Physics Why seat belts can save lives A 75 kg passenger drives a car at 27 m/s (60 mi/h) and does not wear a seat belt. His car crashes into a tree, he flies through the car and is stopped by a hard unpadded dashboard in 0.01s. This force will kill the guy! If he wears a seat belt, Δt is increased to typically about 0.15s. The impulse remains the same, but the force will decrease to 9800 N. This can be survived! WEST VIRGINIA UNIVERSITY Physics Summary • Definition of linear momentum: Unit: kg · m/s Momentum is a vector quantity. It points into the same direction as the object’s velocity. • Relation between momentum and kinetic energy: • Relation between force and impulse: • Definition of impulse: Impulse corresponds to a change of momentum during a time interval Δt. F m vi m vf WEST VIRGINIA UNIVERSITY Physics Conservation of momentum in 1d Two objects (masses: m1, m2) moving at initial velocities v1i and v2i collide. During the time of collision, Δt, object 1 exerts a force F12 on object 2 and object 2 exerts a force F21 on object 1. There are no other external forces! Impulse momentum theorem for m1 and m2: Newton’s third law says: WEST VIRGINIA UNIVERSITY Physics Conservation of momentum in 1d This equations says that the total momentum of the system will be conserved, if there is no effective external force acting on it. Here, the system consists of the two colliding objects. The reason for the conservation of momentum is Newton’s 3rd law, i.e. F12 = -F21. Important: The total momentum is conserved, but not the individual momenta! The momentum (velocities) of the colliding objects typically change as a consequence of the collisions. WEST VIRGINIA UNIVERSITY Physics Example problem: Conservation of momentum The head of a 200 g golf club is traveling at 55 m/s just before it strikes a 46 g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 40 m/s. Find the speed of the golf ball just after impact. WEST VIRGINIA UNIVERSITY Physics Example problem: Astronaut in space An astronaut in his/her space suit has a total mass of 87 kg, including suit and oxygen tank. His/her tether line loses its attachment to her spacecraft, while he/she is on a spacewalk. Initially at rest with respect to her spacecraft, she throws her 12 kg oxygen tank away from her spacecraft with a speed of 8 m/s to propel herself back toward it. Determine the maximum distance she can be from the craft and still return within 2 min (the amount of time the air inside her helmet remains breathable). WEST VIRGINIA UNIVERSITY Physics Conservation of momentum in 2d If the objects can move in 2 dimensions and external forces can be neglected, the equation for momentum conservation will become a vector equation: The momentum is then conserved for every component separately. In this case: x-component: y-component: WEST VIRGINIA UNIVERSITY Physics Example problem: Collision at an Intersection A car with mass 1500 kg traveling east at a speed of 25 m/s collides at an intersection with a 2500 kg van traveling north at a speed of 20 m/s. After the collisions both cars stick together and the resulting wreckage propagates at a common speed. Find the magnitude and the direction of of the velocity of the wreckage. Neglect Friction, i.e. any external forces. WEST VIRGINIA UNIVERSITY Physics Summary • If no effective external force acts on a system of objects, its total momentum will be conserved. • • In 2d, this equation becomes a vector equation and momentum conservation is valid for each component separately. • Conservation of momentum can be explained by by Newton’s third law, i.e. all internal forces compensate each other. • Momentum conservation can be used to describe collision processes, i.e. calculate initial and final velocities of the collision partners. WEST VIRGINIA UNIVERSITY Physics