Chapter 7 Impulse and Motion
(a) Can a single object have a kinetic energy and no momentum? (b) Can a group of two or more objects have a total kinetic energy that is not zero but a total momentum that is zero?
(A) No; (B) Yes
Two balls collide in a one-dimensional elastic collision. The two balls constitute a system, and the net external force acting on them is zero. The table shows four possible sets of values for the initial and final momenta of the two balls, as well as their initial and final kinetic energies. Only one set of values could be correct. Which is it?
(D)
On a distant asteroid, a large catapult is used to throw chunks of stone into space. Could such a device be used as a propulsion system to move the asteroid closer to the earth?
(YES) The asteroid will move in the direction opposite the direction in which the chunks of stone were thrown.
An airplane is flying horizontally with a constant momentum during a time interval Δt. (a) Is there a net impulse acting on the plane during this time? Use the impulse-momentum theorem to guide your thinking. (b) In the horizontal direction, both the thrust generated by the engines and air resistance act on the plane. Considering your answer to part (a), how is the impulse of the thrust related in magnitude and direction to the impulse of the force due to the air resistance?
(a) No, because the momentum is constant. (b) The impulse of the thrust is equal in magnitude and opposite in direction to the impulse of the force due to air resistance. In this way, the net impulse is zero.
A sunbather is lying on a floating raft that is stationary. She then gets up and walks to one end of the raft. Consider the sunbather and raft as an isolated system. (a) What is the velocity of the center of mass of this system while she is walking? (b) Does the raft itself move while she is walking? If so, what is the direction of the raft's velocity relative to that of the sunbather?
(a) The velocity of the center of mass of the system is zero since momentum is conserved. (b) The direction of the raft's velocity relative to the sunbather is opposite the motion of the sunbather because the momentum of the system is zero.
A satellite explodes in outer space, far from any other body, sending thousands of pieces in all directions. Is the linear momentum of the satellite before the explosion less than, equal to, or greater than the total linear momentum of all the pieces after the explosion?
(equal to) According to the principle of conservation of linear momentum, the linear momentum is conserved in this case because there are no external forces acting on the system.
A Collision
A situation in which two objects in close contact exchange energy and momentum. 1.Internal forces: Forces that the objects within the system exert on each other. 2.External forces: Forces exerted on the objects by agents external to the system.
Suppose you are standing on the edge of a dock and jump straight down. If you land on sand your stopping time is much shorter than if you land on water. Using the impulse-momentum theorem as a guide, determine which one of the following statements is correct.
Because the impulse is the same in both scenarios, the average force multiplied by the elapsed time will be the same. The sand will exert a larger average force since the elapsed time is shorter.
In an elastic collision, the kinetic energy of each object is always the same before and after the collision.
False
An object slides along the surface of the earth and slows down because of kinetic friction. If the object alone is considered as the system, the kinetic frictional force must be identified as an external force that, according to Equation 7.4, decreases the momentum of the system. (a) If both the object and the earth are considered to be the system, is the force of kinetic friction still an external force? (b) Can the frictional force change the total linear momentum of the two-body system?
In this case, the frictional force is no longer external. Total momentum is conserved for the two bodies since the frictional forces are internal. (A)=No (B)=NO
An ice boat is coasting on 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 into the boat, which continues to coast straight ahead. (a) Does the total horizontal momentum of the boat plus the jumper change? (b) Does the speed of the boat itself increase, decrease, or remain the same?
Linear momentum in the horizontal direction is conserved, so the total linear momentum in the horizontal direction remains the same. The speed of the boat must decrease to conserve momentum because the mass moving horizontally increases. (A):No (B): Decrease
Inelastic collision
Linear momentum is conserved but it is One in which the total kinetic energy of the system is not the same before and after the collision; if the objects stick together after colliding, the collision is said to be completely inelastic.
two-dimensional collisions
Momentum is a vector quantity meaning it has direction and magnitude.
In movies, Superman hovers in midair, grabs a villain by the neck, and throws him forward. Superman however, remains stationary. This is not possible, because it violates which one or more of the following?
Newton's second law Newton's third law The principle of conservation of linear momentum
Elastic collision
One in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision. Kinetic Energy and total linear momentum are conserved (KE)in1+(KE)in2=(KE)final1+(KE)final2
You are a passenger on a jetliner that is flying at a constant velocity. You get up from your seat and walk toward the front of the plane. Because of this action, your forward momentum increases. Does the forward momentum of the plane itself decrease, remain the same, or increase?
Since linear momentum is conserved, the sum of the changes in the linear momenta of the plane and you must be equal to zero.
Kinetic losses of energy
Sound Friction Heat
Center of mass (along a straight line)
The center of mass is a point that represents the average location for the total mass of a system.
DEFINITION OF IMPULSE
The impulse J→ of a force is the product of the average force F→ and the time interval Δt during which the force acts: Impulse is the change in momentum. SI Unit of Impulse: newton · second (N · s)
DEFINITION OF LINEAR MOMENTUM
The linear momentum p→ of an object is the product of the object's mass m and velocity
Water, dripping at a constant rate from a faucet, falls to the ground. At any instant there are many drops in the air between the faucet and the ground. Where does the center of mass of the drops lie relative to the halfway point between the faucet and the ground?
The spacing between drops increases as the drops fall toward the ground. Therefore, at any given time, there's more mass above the halfway point.
PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM
The total linear momentum of an isolated system remains constant (is conserved). An isolated system is one for which the vector sum of the average external forces acting on the system is zero.
Velocity of Center of mass (isolated system)
Total linear momentum is conserved. P1(m1*v1) and P2(m2*v2) reamin constant. velocity(cm) of the center of mass does is the same after the collision.
Impulse-Momentum Theorem
When a net average force ∑F→‾ acts on an object during a time interval Δt the impulse of this force is equal to the change in momentum of the object:
Velocity Center of Mass
X positions are replaced with Δx1 and Δx2. Then both sides are divided by the time interval Δt to obtain a velocity of the center of mass. The numerator is the Momentum of particle 1 plus the Momentum of particle 2.
isolated system
a closed system on which the net external force is zero. Therefore the total initial momentum and final momentum are equal.
DEFINITION OF KINETIC ENERGY
energy of motion
Suppose two objects collide head on, as in Example 7, where initially object 1 (mass = m1) is moving and object 2 (mass = m2) is stationary. Now assume that they have the same mass, so m1 = m2. Which one of the following statements is true?
since the two masses are the same, the final velocity of object one is zero and the final velocity of object two equals the initial velocity of object one. Object 1 stops completely, while object 2 acquires the same velocity (magnitude and direction) that object 1 had before the collision.
