Physics 2A Chapter 7: Impulse and Momentum

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1 Physics 2A Chapter 7: Impulse and Momentum "Remember happiness doesn't depend upon who you are or what you have; it depends solely on what you think. Dale Carnegie Most folks are about as happy as they make up their minds to be. Abraham Lincoln A ship in the harbor is safe, but that is not what ships are built for. William Shedd You miss 100% of the shots that you don t take. Wayne Gretsky Reading: pages Outline: momentum impulse impulse-momentum theorem everyday example of applications of the impulse-momentum theorem law of conservation of momentum collisions in one dimension elastic and inelastic collisions collisions in two dimensions center of mass (read on your own) Problem Solving Most calculations of impulse are rather straightforward. Remember that impulse is a vector quantity and you must, for example, use the x component of the force to find the x component of the impulse. You might also be given sufficient information to calculate the initial and final linear momentum of a particle. Then, use F = t mvf mvi to calculate the impulse. Many problems of this chapter can be worked using the principle of conservation of linear momentum. If you suspect the principle can be used, first check for external forces: if there are none or if they add to zero, total linear momentum is conserved. Write the momentum at the beginning of some interval in terms of the velocities and masses of the particles involved. Do the same for the momentum at the end of the interval. Equate the two expressions and solve for the unknown quantities. Collision problems are more complicated. First decide if the collision is one- or twodimensional. A head-on collision is always one-dimensional. So is a completely inelastic twobody collision with one object initially at rest. If the objects move along different lines, whether initially or finally, the collision is two-dimensional.

2 First consider one-dimensional collisions. Since total linear momentum is always conserved in collisions, nearly every problem solution begins by writing the equation for conservation of linear momentum. There is only one such equation for a one-dimensional collision. Always use symbols, not numbers, even for given quantities. Make a list of the quantities given in the problem statement and a list of the unknowns. If there is only one unknown, the linear momentum conservation equation can be solved immediately for it. For two-dimensional collisions there are two linear momentum conservation equations, one for each component. Select a coordinate system and write the linear momentum conservation equations in terms of the masses, speeds, and angles between the velocities and a coordinate axis. Questions and Example Problems from Chapter 7 Question 1 An ice boat is coasting along a frozen lake. Friction between the ice and the boat is negligible, and so is air resistance. Nothing is propelling the boat. From a bridge, someone jumps straight down and lands in the boat, which continues to coast straight ahead. (a) Does the horizontal momentum of the boat change? (b) Does the speed of the boat increase, decrease, or remain the same? Explain your answers. Problem 1 A kg baseball is dropped from rest. If the magnitude of the baseball s momentum is kg m/s just before it lands on the ground, from what height was it dropped?

3 Problem 2 A 5.0 kg cat is running northward at 4.50 m/s, while at the same time a 20.0 kg dog is running eastward at 3.00 m/s. Their 70.0 kg owner has the same momentum as the two pets taken together. Find the magnitude and direction of the owner s velocity. Problem 3 A 0.14 kg baseball moves horizontally with a speed of 35 m/s towards the bat. After striking the bat the ball moves vertically upward with half its initial speed. Find the direction and magnitude of the impulse delivered to the ball by the bat.

4 Problem 4 A truck of mass 10 4 kg is initially traveling at 35 m/s when it hits the brakes. If the brakes are applied for 2.0 s, what is the average force required to bring it to rest? Problem 5 Two blocks of masses M and 3M are placed on a horizontal, frictionless surface as shown in the figure below. A light spring is attached to one of them, and the blocks are pushed together with the spring between them compressed. A light cord initially holding the blocks together is burned; after this, the block of mass 3M moves to the right with a speed of 2.00 m/s. Find the speed of the block of mass M.

5 Problem 6 A 10 kg block is sliding with a velocity of 5.0 m/s to the right on a frictionless surface when it explodes into two pieces. After the explosion, piece A, with a mass of 7.0 kg, is traveling 2 m/s to the left as shown in the figure below. Find the velocity of piece B assuming that no mass is lost in the explosion. Problem 7 A kg projectile is fired with a velocity of +715 m/s at a 2.00 kg wooden block that rests on a frictionless table. The velocity of the block, immediately after the projectile passes through it, is m/s. Find the velocity with which the projectile exits from the block.

6 Problem 8 In the figure below, block 2 (mass 1.0 kg) at rest on a frictionless surface and touching the end of an unstretched spring of spring constant 200 N/m. The other end of the spring is fixed to a wall. Block 1 (mass 2.0 kg), traveling at speed v 1 = 4.0 m/s, collides with block 2, and the two blocks stick together. When the blocks momentarily stop, by what distance is the spring compressed? Problem 9 A completely inelastic collision occurs between two balls of wet putty that move directly toward each other along a vertical axis. Just before the collision, one ball, of mass 3.0 kg, is moving upward at 20 m/s and the other ball, of mass 2.0 kg, is moving downward at 12 m/s. How high do the combined two balls of putty rise above the collision point?

7 Problem 10 By accident, a large plate is dropped and breaks into three pieces. The pieces fly apart parallel to the floor. As the plate falls, its momentum has only a vertical component, and no component parallel to the floor. After the collision, the component of the total momentum parallel to the floor must remain zero, since the net external force acting on the plate has no component parallel to the floor. Use the data shown in the drawing, find the masses of pieces 1 and 2.

8 Problem 11 A 20.0 kg body is moving in the positive x direction with a speed of 200 m/s when, owing to an internal explosion, it breaks into three parts. One part, with a mass of 10.0 kg, moves away from the point of explosion with a speed of 100 m/s in the positive y direction. A second fragment, with a mass of 4.00 kg, moves in the negative x direction with a speed of 500 m/s. (a) What is the velocity of the third (6.00 kg) fragment? (b) How much energy is released in the explosion? Ignore effects due to the gravitational force.