Ch 09: Momentum & ImpulseWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Example #1: Push-Away With Energy


Hey guys so a few push away problems may also ask you to solve for energy at some point now this is pretty straightforward but we haven't done one yet so let me show you how it happens how it works. So here for example I have a bomb that exploded in the air into two fragments, OK? So this is a classic type of push away problem where you have an object that has two parts and it breaks apart much like a bomb explosion which is the case here one fragment's going to go to one side, the other fragments is going to go the opposite way so this is a push away where 2 parts of the bomb are pushing away from each other as a result of the explosion so I'm going to draw the two parts of the bomb and let's call this part 1 and let's call this part 2, one fragments 3 kilograms in mass and moves with 100 meters per second now it says that its positive so I'm going to assume that positive is to the right so let's say it's this side here, 100....I'm sorry that's 3 kilograms and it's going to move this way with 100meters per second after the explosion, the other fragment is 4 kilograms and it would presumably move to the left it has to move to the left if one moves to the right the other moves to the left but we don't know that velocity so we're going to call it V1 final and that's what we want to know, if the second fragment is 4 kilograms in mass what velocity will it attain, OK? We're going to use conservation of momentum to do this, the big equation here and M1V1+M2V2=M1V1 final+M2V2 final, we use conservation of momentum because we have two parts of an object that are pushing away from each other that's a push of a problem so we use this, let's put the masses I have 4 and 3, notice that there is no references to the initial velocity of this thing it is in the air but it doesn't say if it's moving left or right so you assume that it's not moving otherwise you have to make up a velocity and that's not cool you can't just make up numbers, so we'll assume that it's not moving therefore the initial velocity is 0, right? If it's falling that's fine but it can't be moving left or right it doesn't tell you that so you have to assume it's 0, after the explosion the 3 kilogram moves to the right with a 100 and the 4 is what we want to know so V1final is what we're looking for so let's solve for that, this is 0 and 0 for V1final + 300 and I'm going to move everything out of the way, we get -300/4 is our Vfinal so that's -75 meters per second, I got a negative which means it's going to the left and it makes sense if one fragment explodes the right the other one goes to the left so there's nothing new here, the part that's new is this idea of asking how much energy was stored in the bomb, OK? Now here we have assumed that energy is conserved because it doesn't tell us otherwise so we assume that the energy is conserved so the idea is that the initial energy this is before the explosion equals the final energy which is after the explosion, now again initially it's not moving so it only has potential energy, and at the end it is moving so you have kinetic energy the idea is that the energy stored in is your potential energy, right? you can think of it as your potential energy before the explosion and that's how bombs work it's got some stored energy in there that turns into an explosion and then all of the potential energy becomes kinetic energy that's how all these problems work when it's asking for the store energy in a bomb so all you have to do is solve for K final, 1/2 M1V1 final squared + 1/2 M2V2 final squared, that's it we're going to plug in numbers and we're done, so this is 1/2 (4)(-75 squared) + 1/2(3)(100 squared), those are all the numbers and if you plug everything you get 26250 Joules that is the store energy so the idea is that by knowing what happens at the end of the explosion how fast each piece is moving you can sort of work backwards and deduce and calculate what the initial energy of the explosion was or the stored energy, OK? Stored energy potential energy whatever, cool? Another question another way that this could have been asked it could have been asked as how much work is done during the explosion, it would have been the same thing so the work done during the during the explosion is 26250, in this case the idea is that we would be thinking this is like a separate way we would be thinking of the explosion as work instead of potential energy, OK? But the basic idea is that whatever initial energy will be equal whether you call it stored energy whether you call work it work it will be just kinetic final which is kinetic final of the two parts, however this thing gets called. Hope that makes if you have any questions let me know.

Practice: Two blocks (3 kg and 4 kg) on a smooth floor are pressed against a light spring (force constant 800 N/m) between them. When the blocks are released, the 3 kg is launched with 10 m/s. 

(a) What speed is the 4 kg launched with? 

(b) How much was the spring compressed by before the blocks were released?

Blocks A and B are initially at rest on a horizontal frictionless surface with a spring of negligible mass compressed between them. Block A has mass 5.0 kg and block B has mass 20.0 kg. The spring is released and the blocks move off in opposite directions. After the blocks, have moved away from the spring. A) the magnitude of the momentum of block A is the same as the magnitude of the momentum of block B  B) the magnitude of the momentum of block A is less than the magnitude of the momentum of block B  C) the magnitude of the momentum of block A is greater than the magnitude of the momentum of block B
Two blocks are at rest on a horizontal frictionless surface with a compressed spring of negligible mass between them. Block A has mass 2.00 kg and block B has mass 5.00 kg. The blocks are released from rest and move off in opposite directions, leaving the spring behind. If block B has speed 0.800 m/s after it leaves the spring, what is the speed of block A after it leaves the spring? (Block A is the less massive block.) (a) 0.63 m/s (b) 0.95 m/s (c) 1.00 m/s (d) 1.26 m/s (e) 1.50 m/s (f) 2.00 m/s (g) none of the above answers
A 20.0-kg projectile is fired at an angle of 60.0° above the horizontal with a speed of 80.0 m/s{ m{ m/s}}. At the highest point of its trajectory, the projectile explodes into two fragments with equal mass, one of which falls vertically with zero initial speed. You can ignore air resistance.(a) How far from the point of firing does the other fragment strike if the terrain is level?(b) How much energy is released during the explosion?
A 140 kg astronaut (including space suit) acquires a speed of 2.60m/s by pushing off with his legs from a 1800 kg space capsule.(a) What is the change in speed of the space capsule?(b) If the push lasts 0.505 s, what is the average force exerted by each on the other? As the reference frame, use the position of the capsule before the push.(c) What is the kinetic energy of the astronaut after the push?(d) What is the kinetic energy of the space capsule after the push?
Boxes A and B are at rest on a horizontal frictionless surface with a compressed spring of negligible mass between them. Box a has mass 2.0 kg and box B has 4.0 kg. When the spring is released the two boxes move off in opposite direction and the spring is left behind. After the boxes have moved away from the spring,A) the magnitude of the momentum of A is less than the magnitude of the momentum of BB) the magnitude of the momentum of A is greater than the magnitude of the momentum of BC)  the magnitude of the momentum of A is equals than the magnitude of the momentum of BD) the kinetic energy of A equals the kinetic energy of B
A 65.0-kg boy and his 40.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with velocity 2.90 m/s toward the west. Ignore friction.(a) Describe the subsequent motion of the girl.(b) How much potential energy in the girl’s body is converted into mechanical energy of the boy–girl system?
A cannon is rigidly attached to a carriage, which can move along horizontal rails but is connected to a post by a large spring, initially unstretched and with force constant k = 2.00 X 104 N/m, as shown in the figure. The cannon fires a 200-kg projectile at a velocity of 125 m/s directed 45.0° above the horizontal. Assuming that the mass of the cannon and its carriage is 5000 kg,(a) Find the recoil speed of the cannon.(b) Determine the maximum extension of the spring.(c) Find the maximum force the spring exerts on the carriage.(d) Consider the system consisting of the cannon, carriage, and projectile. Is the momentum of this system conserved during the firing? Why or why not?
Old naval ships fired 13 kg cannon balls from a 230 kg cannon. It was very important to stop the recoil of the cannon, since otherwise the heavy cannon would go careening across the deck of the ship. In one design, a large spring with spring constant 2.5×104 N/m was placed behind the cannon. The other end of the spring braced against a post that was firmly anchored to the ships frame. What was the speed of the cannon ball if the spring compressed 56 cm when the cannon was fired?
An atomic nucleus at rest decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is 2.6×105 m/s? Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.
A 8.50 kg shell at rest explodes into two fragments, one with a mass of 2.50 kg and the other with a mass of 6.00 kg. If the heavier fragment gains 130 J of kinetic energy from the explosion, how much kinetic energy does the lighter one gain?
An atomic nucleus initially moving at 435 m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350 m/s. If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 216 u , what speed does the alpha particle have when it is emitted?
A 226-kg projectile, fired with a speed of 126 m/s at a 61.0   angle, breaks into three pieces of equal mass at the highest point of its arc (where its velocity is horizontal). Two of the fragments move with the same speed right after the explosion as the entire projectile had just before the explosion; one of these moves vertically downward and the other horizontally.(a) Determine the magnitude of the velocity of the third fragment immediately after the explosion.(b) Determine the direction of the velocity of the third fragment immediately after the explosion.(c) Determine the energy released in the explosion.
An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.7 times the mass of the other. If 7300 J is released in the explosion, how much kinetic energy does each piece acquire?