Center of mass and momentum Questions and Answers

An 0 010 kg bullet is fired down the barrel of a gun which is pointed to the left The bullet accelerates from rest to a velocity of 400 What velocity does the 1 5 kg gun acquire as a result of this impulse Note that neither the bullet nor the gun was moving before the collision Final P Initial Impulse P P Change in Momentum O R

Dynamics cart 1 has a mass of 0 84 kg and is initially moving at 4 2 m s right Cart 1 undergoes an elastic head on collision with dynamics cart 2 The mass of cart 2 is 0 48 kg and cart 2 is initially moving at 2 4 m s left The collision is cushioned by a spring with spring constant 8 0 3 103 N m T I a Calculate the velocity of each cart immediately after the first collision b Determine the compression of the spring during the collision at the moment when cart 1 is moving at 3 0 m s right c Determine the maximum compression of the spring

A neutron of mass 1 7 x 10 27 kg travelling at 2 2 km s hits a stationary helium nucleus of mass 6 6 x 10 27 kg After the collision the velocity of the helium nucleus is 0 53 km s at 52 to the original direction of motion of the neutron Determine the final velocit of the

Your classmate makes the following statement For a head on elastic collision between two object of equal mass the after collision velocities of the objects are at right angles to each other Evaluate the accuracy of this statement A

A hockey puck of mass 0 16 kg sliding on a nearly frictionless surface of ice with a velocity of 2 0 m s E strikes a second puck at rest with a mass of 0 17 kg The first puck has a velocity of 1 5 m s N 31 E after the collision Determine the velocity of the second puck after the collision A

1 Two balls of equal mass undergo a collision see Figure 6 Ball 1 is initially travelling horizontally with a speed of 10 0 m s and ball 2 is initially at rest After the collision ball 1 moves away with a velocity of 4 7 m s at an angle of 60 0 from its original path and ball 2 moves away at an unknown angle d Determine the magnitude and direction of velocity of ball 2 after the collision V 0 m s 2 1 a 10 0 m s b V 4 7 m s 2 6 8 60 0

A carbon 14 nucleus initially at rest undergoes a nuclear reaction known as beta decay The nucleus emits two particles horizontally one with momentum 7 8 x 10 21 kg m s E and another with momentum 3 5 x 10 2 1 kg m s S a Calculate the direction of the motion of the nucleus immediately following the reaction b Determine the final momentum of the nucleus c The mass of the residual carbon 14 nucleus is

Two hockey pucks of equal mass approach each other Puck 1 has an initial velocity of 20 0 m s S 45 E and puck 2 has an initial velocity of 15 m s S 45 W After the collision the first puck is moving with a velocity of 10 0 m s S 45 W U a Determine the final velocity of the second puck b Is this collision elastic perfectly inelastic or non perfectly inelastic Explain your reasoning

An automobile collides with a truck at an intersection The car of mass 1 4 10 kg is travelling at 32 km h S the truck has a mass of 2 6 X 10 kg and is travelling at 48 km h E The collision is perfectly inelastic Determine their velocity just afte the collision

3 Frictional forces are large for colliding vehicles during a car crash Is conservation of momentum 5 4 still useful in analyzing these crashes MCOBJ

2 A block of ice of mass 50 0 g slides along a frictionless frozen lake at a speed of 0 30 m s It collides with a 100 0 g block of ice that is sliding in the same direction at 0 25 m s The two blocks stick together a Draw a diagram of the system before and after the collision b How fast are the two blocks moving after the collision c How much kinetic energy is lost

Exercise 7 18 A constant force F acts on a particle of mass m initially at rest What is 0 t its rapidity at time t Force is still the rate of change of the relativistic momentum p Start with p in terms of 0 Give the answer in terms of an inverse hyperbolic function Show that for large times we may approximate 0 t In 2Ft m

1 A 1 4 x 10 kg car is westbound at a velocity of 37 0 km h when it collides with a 2 0 x 10 kg truck northbound at a velocity of 35 km h If these two vehicles lock together upon collision what is the initial velocity of the vehicles after collision 7 2 m s 37 W of N

4 A 50 0 kg object is moving east at an unknown velocity when it collides with a 60 0 kg stationary object After collision the 50 0 kg object is traveling at a velocity of 6 0 m s 50 0 N of E and the 60 0 kg object is traveling at a velocity of 6 3 m s 38 S of E a What was the velocity of the 50 0 kg object before collision b Determine whether this collision was elastic or inelastic 9 86 m s due east Ek loss of 340 J so inelastic

6 A watermelon explodes into three equal masses One mass moves east at 15 0 m s If a second mass moves at a velocity of 10 0 m s 45 0 S of E what is the velocity of the third mass Hint the total momentum is zero so how will your vector arrows add up

embedded in the edge of a solid disk of mass M 3 2kg and radius R 0 5m The cylinder is free to rotate around its axis and is initially at rest What is the angular velocity of the disk immediately after the bullet is embedded Moment of inertia of the disk I MR 1 2 rad s O 6 5 rad s O 1 7 rad s O 0 58 rad s O 0 14 rad s O2 45 rad s 500 m s to

5 A bullet with a mass of 45 g is fired into a 8 3 kg block of wood resting on a floor against a spring This ideal spring k 76 N m has a maximum compression of 28 cm What was the initial speed of the bullet A 8 marks

is conserved for all collisions served conserved although 5 Two skaters are studying collisions on an ice covered frictionless lake Skater 1 has a mass of 95 kg and is initially travelling with a speed of 5 0 m s and skater 2 has a mass of 130 kg and is initially at rest Skater 1 then collides with skater 2 and they lock arms and travel away together K a Does the system undergo an elastic collision or an inelastic collision Explain your answer unlocity of the two skaters 50 26

Two people are riding inner tubes on an ice co frictionless lake The first person has a mass a 85 kg and is travelling with a speed of 6 5 m s collides head on with the second person with a mass of 120 kg who is initially at rest They bou apart after the perfectly elastic collision The fir velocity of the first person is 1 1 m s in the opp direction to his initial direction KTA CA a Are momentum and kinetic energy conser for this system Explain your answer b Determine the final velocity of the second pe

Explain how this The particles in Figure 6 undergo an elastic collision in one dimension Particle 1 has mass 1 5 g and particle 2 has mass 3 5 g Their veloci before the collision are 12 m s right and 7 5 m s left Determine the velocity of two particles after the collision K TA A V Vi 12

pizza chef tosses a spinning ball of dough into the air The centrifugal force produced by the spin causes the dough to stretch out from a spherical ball to a flat diske uring this process which of the following quantities remain constant heck all that apply there may be more than one correct answer mass angular momentum moment of inertia angular velocity

A 31 3 kilogram child on a skateboard is traveling at a speed of 8 29 m s when he collides head on with his 85 1 kilogram father who is standing at rest The two grab each other thereby sticking together in the collision Immediately after the collision is complete what is the final speed in meters second of the father and child together m s Hint Your final answer should be between 0 5 and 5 m s

Work each of the following problems SHOW ALL WORK 1 A 1 kg blob of clay moving at 8 m s collides inelastically with a 3 kg wooden block that is initially at rest a What is the initial momentum of the system b What must be the final momentum of the system Date c Calculate the velocity of the blob and block immediately after the collision 2 A 1 250 kg car is stopped at a traffic light A 3 550 kg truck moving at 8 33 m s hits the car from behind a What is the initial momenturn of the system b What must be the final momentum of the system c If the bumpers of the car and truck lock how fast will the two vehicles moun tonot

DR C H 5 0 m b 9m d e H 5 0 m 7 777777 7777 C1992M1 A ball of mass 9m is dropped from rest from a height H 5 0 meters above the ground as shown above on the left It undergoes a perfectly elastic collision with the ground and rebounds At the instant that the ball rebounds a small blob of clay of mass m is released from rest from the original height H directly above the ball as shown above on the right The clay blob which is descending collides with the ball 0 5 seconds later which is ascending Assume that g 10 m s that air resistance is negligible and that the collision process takes negligible time T a Determine the speed of the ball immediately before it hits the ground Determine the rebound speed of the ball immediately after it collides with the ground justify your answer Determine the height above the ground at which the clay ball collision takes place 9m Determine the speeds of the ball and the clay blob immediately before the collision If the ball and the clay blob stick together on impact what is the magnitude and direction of their velocity immediately after the collision

pendicular to each other until they collide Figure below Particle 1 has mass 2m and momentum of magnitude 2p and particle 2 has mass 3m and momentum of magnitude p Note Magnitudes are not drawn to scale in any o the figures Suppose that after the collision the particles trade their momenta as shown in the figure That is particle 1 now has magnitude of momentum p and particle 2 has magnitude of momentum 2p furthermore each particle is now moving in the direction in which the other had been moving How much kinetic energy Klost is lost in the collision O O O Before collision 3p 4m 3p 4m 7p Gen 2m 4m 2p p p 2m 3m After collision 3m 2p

Two objects with the same mass move toward each other with the same speed and experience an elastic collision Compare the final velocities of each object to their initial velocities

10 points Three different mass balls are moving on a large soccer field Ball 1 has a mass of 6 76 kg and is moving with a velocity of 9 35m to the right Ball 2 has a mass of 10 21 kg and is moving with a velocity of 7 17 to the left m S Ball 3 has a mass of 7 34 kg and is moving with a velocity of 1 25 down m S What is the group momentum of the 3 balls 2 7 kg 9 1 kg O O 10 0 kg m S 10 0 kg 15 4 kg O 2 7 kg 2 7 kg 15 4 kg m S 2 7 kg 2 7 kg 15 4 kg m S m S m S m S m S m S m S x 8 T 9 1 kg m S m S 3 8 kg 9 1 kg 10 0 kg 14 1 kg x 14 1 kg m S m S m 3 8 kg T S m S 14 1 kg 3 8 kg my S m S m S

2006B2B 1 5M A small block of mass M is released from rest at the top of the curved frictionless ramp shown above The block slides down the ramp and is moving with a speed 3 5v when it collides with a larger block of mass 1 5M at rest at the bottom of the incline The larger block moves to the right at a speed 2 v immediately after the collision Express your answers to the following questions in terms of the given quantities and fundamental constants a Determine the height of the ramp from which the small block was released b Determine the speed of the small block after the collision c The larger block slides a distance D before coming to rest Determine the value of the coefficient of kinetic friction u between the larger block and the surface on which it ides d Indicate whether the collision between the two blocks is elastic or inelastic Justify your answer

A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally see figure The ball is covered with glue so it sticks to the bar During this collision Hook O both the angular momentum of the system ball and bar and its kinetic energy are conserved O both the linear momentum and the angular momentum of the system ball and bar are conserved O the angular momentum of the system ball and bar is conserved about the hook because only gravity is acting on the system O the angular momentum of the system ball and bar is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook 23

Two cylinders of the same size and mass roll down an incline Cylinder A has most of its weight concentrated at the rim while cylinder B has most of its weight concentrated at the center Which reaches the bottom of the incline first OA OB O it is a tie can t be determined

10 points A 6 pounder field gun cannon used during the American Civil War has a mass of 405 kg and uses cannonball with a mass of 2 40 kg If the cannonball is fired with a speed of 470 m what is the recoil speed of the cannon O 3 7 O O m S 2 1 m S 0 5 m S

Please rank the following objects momentum from greatest to least Greatest 1 2 3 4 A1 24 x 105 kg helicopter hovering in mid air at rest A55 kg person running at 1 2 m S A 0 02 kg bullet moving at 950 m S A0 63 kg basket ball moving at 3 5 m S

10 points A 0 099 kg bouncy ball is dropped from a certain height and reaches a speed of 6 3m right before it bounces on the ground S If the ball bounces upwards with a speed of 3 8 m what was the impulse supplied by the ground O O O 1 00 N s 2 02 N s 0 26 N s 1 85 N S

10 points Two balls are traveling towards each other an have an inelastic collision S Ball A has a mass of 3 1 kg and a velocity of 1 00 m to the right while ball B has a mass of 1 9 kg and a velocity of 1 80m to the left After the collision ball A has a velocity of 0 50 the left Find the velocity of ball B and use that to find out the group total final kinetic energy O 7 7 J O 2 5 J O 0 8 J D 0 m S to

A rubber ball and a lump of clay have equal mass They are thrown with equal speed against a wall The ball bounces back with nearly the same speed with which it hit The clay sticks to the wall Which one of these objects experiences the greater momentum change A B C D the clay Both of them experience the same non zero momentum change Both of them experience zero momentum change the ball

A steel ball weighing 190 lbs slides on a flat horizontal floor surface and strikes a stationary wooden ball weighing 180 lbs If the steel ball has a velocity of 16 1 ft s impact what is its velocity immediately after impact Assume a frictionless floor and the collision is perfectly elastic Round your answer to 2 decimal places

2788074 3 n jpg Question 13 Add your answer A steel ball weighing 213 lbs slides on a flat horizontal floor surface and strikes a stationary wooden ball weighing 206 lbs If the steel ball has a velocity of 15 8 ft s impact what is its velocity immediately after impact Assume a frictionless floor and the collision is perfectly elastic Round your answer to 2 decimal places 2701522 2790894 9 n jpg 2 ning 2701050 A 3 Points ing

Question 2 Whether a truck comes to a stop by crashing into a haystack or a brick wall the stopping force is A greater with the haystack B greater with the brick wall C both the same Screens 17 png Screens 18 png 2 F

Q1 A car with a mass of 1100 kg is travelling at a speed of 33 m s Determine the magnitude of the total momentum

28 A 0 24 kg blob of clay strikes a wall at speed O 26 N O 51 N O 42 N O 35 N 16 m s The clay comes to a stop in 91 ms What is the average force that the wall exerts on the clay

For a system consisting of two particles that undergo an elastic collision momentum is conserved but Kinetic energy is not conserved O both kinetic energy and momentum are conserved neither the total energy nor momentum is necessarily conserved O kinetic energy is conserved but momentum is not conserved neither the kinetic energy nor momentum is conserved

A 1200 kg car moving at 15 6 m s collides with a stationary car of mass 1500 kg If the two vehicles lock together what is their combined velocity immediately after the collision 12 1 m s 6 9 m s 8 6 m s 5 5 m s

A handball of mass 0 180 kg traveling horizontally at 29 0 m s strikes a wall and rebounds at 18 0 m s What is the magnitude of the impulse in Ns imparted on the ball Your Answer

p mv ElasticCollisions KE m U mgh U kx Wtric Fried Fine N E KE U U E W c Ej Wiric v V2 v 5 V F Fo vost zast v voz a t Problem 1 A ball of mass m 0 44 kg is moving to the right in the r direction with a speed 13 3 m sec collides head on with a mass m 0 22 kg at rest If the collision is perfectly elastic what vill be the speed and direction of each ball after the collision Answer v 11 m sec to the right and 124 4 m sec to the right

A 2 05 x 105 kg runaway steam locomotive is heading for a baby lying on the tracks at 25 m s Mighty mouse wants to fly head on into the train to stop it If Mighty Mouse is 50 grams how fast does he have to fly into the train to stop it using his momentum alone Assume the train s structural integrity is strong enough to take the blow To this possible Include all steps

m 1 56 kg ball traveling rest What was the final velocity of the system 4 6 horizontally landed in a 22 kg wheeled cart that began at

after before A block of mass m 12 kg travels from left to right across a frictionless surface at constant speed V Just ahead of it is a second block of mass M 88 kg that travels at a speed 0 9 m s 0 5 m s of in the same direction Then the blocks collide and stick together traveling at a new speed of 12 kg block During the collision what is the impulse of the force on the O 79 N s to the left O 62 N s to the left O 44 N s to the right

6 Incorrect Tries 1 8 Previous Tries 0 2 V 4 6 t s 12 p67 The figure gives as a function of time t the force component Fx that acts on a 3 kg ice block that can move only along the x axis At t 0 the block is moving in the positive Etion of the axis with a speed of 5 m s What is the velocity at t 11 s use the sign as the indication of direction s bmit Answer

H O 02 X L hrw8c9p5 A cubical box open at the top with edge length 68 cm is constructed from metal plate of uniform density and negligible thickness see the figure Find the z the center of mass of the box cm

hrw8c9p92 A body of mass 6 0 kg is traveling at 3 3 m s along the positive x axis with no external force acting At a certain instant an internal explosion occurs splitting the boc two chunks of 3 0 kg mass each The explosion gives the chunks an additional 16 J of kinetic energy Neither chunk leaves the line of original motion Determine the speed and dir of motion of each of the chunks after the explosion Enter the larger velocity Submit Answer Tries 0 8 Enter the smaller velocity