Ch 7 - Momentum and Impulse

A 0.350 kg lump of clay is dropped from a height of 1.15 m onto the floor. It sticks to the floor and does not bounce. What is the magnitude of the impulse J imparted to the clay by the floor during the impact? Assume that the acceleration due to gravity is g = 9.81 m/s^2. The force exerted by the floor on the clay is plotted as a function of time in the figure (total time that the clay was in contact with the floor is 9.5 ms; maximum force is achieved in half that time). What must have been the max force exerted by the floor on the clay?

J = 1.66 kg x m/s Fmax = 350 N

Fill in the blanks with less than, greater than, the same as, or I don't know: Object A is initially at rest. Object B is initially moving, and it collides with and bounces off object A. Just after the collision the magnitude of the total momentum of the system of two objects will be ( ) magnitude of the total momentum of this system just before the collision. In addition just after the collision the total kinetic energy of the system of two objects will be ( ) this total kinetic energy of this system just before the collision.

The same as, I don't know *just because momentum is conserved does not necessarily mean that kinetic energy is also conserved - both elastic and inelastic collisions conserve momentum, however elastic collisions also conserve mechanical energy whereas inelastic collisions don't*

A bouncy rubber ball and a wet lump of clay, both of mass m, are thrown at a wall. Both strike the wall at speed v, but although the ball bounces off with no loss of speed, the clay sticks. What are the changes in momentum of the clay and ball, respectively? a) mv; 2 mv b) 0; 2mv c) 0;mv d) mv;0 c) mv;mv

a)

Object A has mass 1.00 kg, and object B has mass 3.00 kg. At the instant shown in the figure, the center to center distance between the two objects is 4.00 m, object A is moving to the right at 2.00 m/s, and object B is at rest. No external forces act on the system of the two objects. a) Before the collision, where is the center of mass of the two objects? b) At the instant described above, what is the velocity (magnitude and direction) of the center mass of the two objects? c) Objects A and B collide and stick together. How does this affect the velocity of the center of mass of the two objects?

a) 3.00 m b) +0.50 m/s c) The center of mass velocity does not change, as no external force is acting on the system (A + B)

A boy roller skating at a constant velocity of 2 m/s bounces back at a constant velocity of 1 m/s. In what direction is the boy's change in momentum? a) zero b) in the +x direction c) in the -x direction

b)

Consider the collision between two toy carts sliding on a very smooth surface (one blue cart to the left and a pink cart to the right). The mass of the blue cart is m and the mass of the pink cart is 4m. Initially, the blue toy cart moves to the right at speed v, and the pink toy cart is at rest. After the collision, the speed of both toy carts is v/3 in opposite directions. Was the collision elastic? a) yes b) no What can be said about the velocity of the center of mass of the system of the two toy carts just before and just after the collision? a) the velocity of the center of mass before the collision is greater than the velocity of the center of mass after the collision. b) the velocity of the center of mass before the collision is less the an the velocity of the center of mass after the collision. c) the velocity of the center of mass before the collision is the same as the velocity of the center of mass after. d) the velocity of the center of mass is always zero.

b) c)

The mass of a pigeon hawk is twice that of the pigeon it hunts. A pigeon is gliding north at a speed of Vp = 23.0 m/s when a hawk swoops down, grabs the pigeon, and flies off, as shown in the figure. The hawk is flying north (positive x direction) and down (negative y direction) at a speed of VH= 35.0 m/s, at an angle of 45 degrees below the horizontal, at the instant of the attack. Conservation of momentum can be used to find the final velocity of the pigeon-hawk system, just after the hawk grabs the pigeon, because, a) the force of gravity cancels the drag force due to air b) while the hawk latches on to the pigeon, the force between the birds are much stronger than any other external force acting on the birds. c) the hawk gently latches on to the pigeon Just after the hawk grabs the pigeon, the velocity of the the two birds will point a) up and north b) up and south c) down and north d) down and south

b) c)

Identical balls are dropped from the same initial height and bounce back to half the initial height. In case 1, the ball bounces off a cement floor, and in Case 2, the ball bounces off a piece of stretchy rubber. In which case is the magnitude of the ball's change in momentum greatest? a) Case 1 b) Case 2 c) same in both In which case is the average force acting on the ball during the collision is the biggest? a) case 1 b) case 2 c) same in both

c) a)

A friend throws a heavy ball toward you while you are standing on smooth ice. You can either catch the ball, or deflect it toward your friend. What should you do in order to maximize your speed right after you interaction with the ball? a) you should let the ball go past you without touching it. b) it does not matter; your speed is the same regardless of what you do. c) you should catch the ball. d) more information is required to determine how to maximize your speed. e) you should deflect the ball back toward your friend.

d)

A system of four particles moves along one dimension. The center of mass of the system is at rest, and the particles do not interact with any objects outside of the system. Find the velocity v4 of particle 4 at t1 = 2.59 s given the details for the motion of particles 1-3. Particle 1: m1 = 1.93 kg, v1 (t) = (6.75m/s) + (0.255 m/s^2)xt Particle 2: m2 = 2.57kg, v2(t) = (8.05 m/s) + (0.525 m/s^2)xt Particle 3: m3 = 4.13 kg, v3(t) = (6.99 m/s) + (0.153 m/s^2)xt Particle 4: m4= 5.27 kg

v4 = -13.1 m/s

Four beads, each of mass 1 kg, are attached at various locations to a ring, also of mass 1 kg and radius of 1 m. Find the coordinates of the center of mass of the system consisting of the ring and the beads. Angle A, located between the first bead and the horizontal, is equal to 49 degrees. Angle B, located between the horizontal and second bead, is equal to 50 degrees. Angle C, located between the third bead and the horizontal, is equal to 72 degrees. Angle D, located between the horizontal and the fourth bead, is equal to 33 degrees. xcm? ycm?

xcm = 0.0302 m ycm = -0.0836 m

Two manned satellites approach one another at a relative velocity of v = 0.170 m/s. intending to dock. The first has a mass of m1 = 4.00 x 10^3 kg and the second a mass of 7.50 x 10^3 kg. If the two satellites collide elastically rather than dock, what is their final relative velocity?

-0.170 m/s Mechanical energy is conserved

Calculate the final velocity right after a 113 kg rugby player who is initially running at 7.25 m/s collides head on with a padded goalpost and experiences a backward force of 18500 N for 5.50 x 10^-2s.

-1.75 m/s

A bullet with a mass of 13.5 g is fired into a block of wood at a velocity of 253 m/s. The block is attached to a spring that has a spring constant k of 205 N/m. The block and bullet continue to move, compressing the spring by 35.0 cm before the whole system momentarily comes to a stop. Assuming that the surface on which the block is resting is frictionless, determine the mass of the wooden block.

0.451 kg

A 0.300 kg toy car moving with a speed of 0.820 m/s collides with a wall. The figure shows the force exerted on the car by the wall over the course of the collision. What is the magnitude of the velocity, or final speed, of the car after the collision?

0.480 m/s

An unfortunate astronaut loses his grip during a spacewalk and finds himself floating away from the space station, carrying only a rope and a bag of tools. First he tries to throw a rope to his fellow astronaut, but the rope is too short. In a last ditch effort, the astronaut throws his bag of tools in the direction of his motion, away from the space station. The astronaut has a mass of 113 kg and the bag of tools has a mass 19.0 kg. If the astronaut is moving away from the space station at an initial velocity of 1.80 m/s, what is the minimum final speed of the bag of tools with respect to the space station that will keep the astronaut from drifting away forever?

12.5 m/s

Blythe and Geoff are ice skating together. Blythe has a mass of 45.0 kg, and Geoff has a mass of 89.0 kg. Blythe pushes Geoff in the chest when both are at rest, causing Geoff to move away at a speed of 4.50 m/s. What is Blythe's speed after she pushes Geoff? In what direction does Blyth move? a) in the same direction as Geoff b) in the opposite direction of Geoff

8.90m/s b)