Share
Explore BrainMass

Conservation of Momentum

Momentum is the product of the mass and velocity of an object. For example, a large rock falling down a hill has a larger momentum than a small rock falling down the same hill. Like velocity, momentum is a vector quantity. The equation is as followed:

P=mv

For example, if two particles interact, the forces between them are equal and opposite. If the particles are numbered 1 and 2, the second law states that F1 = dp1/dt and F2 = dp2/dt, therefore:

(dp_1 )/dt= -(dp_2)/dt

And

d/dt ( p_1+ p_2 )= 0

If the particles velocities are u1 and u2 before the interaction and v1 and v2 after the interaction then:

m_1 u_1+ m_2 u_2= m_1 v_1+ m_2 v_2

This law is an exact law which holds true in all situations.
Momentum is a conserved quantity in a closed system. It was first postulated in Newton’s laws of motion. It is now used in many different aspects of scientific calculations. Conservation of momentum is used in collisions, vacuums, quantum mechanics and many more. It has led to many discoveries in the field of physics.

Linear Momentum: Predict Inelastic Collision

You have 2 gliders, a big (subscript b) one with mass mb = 320 grams, and a small (subscript s) one with mass ms = 70 grams. Both gliders are free to move on a horizontal air track on which friction is negligible. Assume that the collisions below are perfectly inelastic because the gliders stick together when they collide. Use

Kinetic Energy Lost in a Vehicle Collision

A car of mass m, traveling with a velocity v, strikes a parked station wagon, whose mass is 2m. The bumpers lock together in this perfectly inelastic head-on collision. What fraction of the initial kinetic energy is lost in this collision? Please provide detailed explanation.

Perfectly Inelastic Collision of Masses

A 2.0-kg mass moves with a speed of 5.0 m/s. It collides head-on with a 3.0 kg mass at rest. If the collision is perfectly inelastic, what is the speed of the masses after the collision? Please provide detailed explanation.

Application of momentum conservation

You are a 50-kg mass skater who skates on ice at 4.0 m/s to greet your 40-kg friend, who is standing still, with open arms. As you collide, while holding each other, with what speed to you both move off together? Please provide detailed explanation

Friction force, impulse momentum, mass and speed, direction

1. A sled and rider, gliding over horizontal, frictionless ice at 4.1 m/s, have a combined mass of 70 kg. The sled then slides over a rough spot in the ice, slowing down to 2.6 m/s. What impulse was delivered to the sled by the friction force from the rough spot? 2. Use the impulse-momentum theorem to find how long (number

An exercise with linear momentum and balls colliding

A stationary ball with a mass of 1.6kg, is struck by an identical ball moving with a velocity of 3m/sec. After the collision the two balls stick together and contiue moving in a straight line, what is the final velocity?

Physics: Momentum Problems

** Please see the attached file for the complete problem description with the diagram ** Please provide a stepwise solution. A system consists of a circular disc (Md=6kg, Rd=2m), onto which is affixed a rectangular block (Mb=4kg, Lb=3m), as shown in the figure below. The system starts at rest. the moment of inertia for the r

Physics: Trajectory of a Projectile

** Please see the attached file for the complete problem description ** Please provide a step-wise solution. A projectile (m=2kg) is shot from a cannon at an initial angle of θ=30° with an initial speed of vo=40m/s. Assume the ball is shot from the origin.

Kinetic friction between ice and car tires

24. A 0.30 kg puck, initially at rest on a frictionless horizontal surface, is struck (inelastically) by a 0.20 kg puck that is initially moving along the x-axis with a velocity of 2.0 m/s. After the collision, the 0.20 kg puck has a speed of 1.0 m/s at an angle of 53° to the +x-axis. Determine the magnitude and direction of th

Determine where the arrow and target connect

A 1000g arrow is launched with a velocity of 40.0 m/s, 30.0 degrees from x=0. At the same time a 400g target is launched with a velocity of 20.0 m/s, 90 degrees from the position of x=60.0 meters. Both objects are launched from ground level. The arrow pierces the target and sticks in it. Determine where the arrow/target (become

Conservation of linear momentum.

A compressed spring is placed with a light adhesive between the large car and the small car such that it is touching the facing ends. The binding of the spring is removed and the two cars are thrust from each other with the spring no longer attached to either. What is the ratio of the speed of the smaller car to that of the larg

Determining the Speed of a Bullet

A 3.5 g bullet is fired horizontally at two blocks at rest on a frictionless tabletop. The bullet passes through the first block with mass of 1.20 kg. and embeds itself in the second, with a mass of 1.80 kg. Speeds of 0.630 m/s and 1.40 m/s, respectively, are thereby given to the blocks. Neglecting the mass removed from the fi

Physics Problems: Conservation of Momentum

See attached figure. In a shipping company distribution center, an open cart of mass 53.0 kg is rolling to the left at a speed of 5.40 m/s (see the figure ). You can ignore friction between the cart and the floor. A 14.0 kg package slides down a chute that is inclined at 37 degrees from the horizontal and leaves the end of

Center of mass of two-stone system moving; speed after impact

A stone is dropped at t = 0. A second stone, with 3 times the mass of the first, is dropped from the same point at t = 190 ms. (a) How far below the release point is the center of mass of the two stones at t = 440 ms? (Neither stone has yet reached the ground.) (b) How fast is the center of mass of the two-stone system moving at

Carousel and its Rotation

A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 125 kg·m2. When one person is standing on the carousel at a distance of 1.50 m from the center, the carousel has an angular velocity of 0.600 rad/s.

Billiard ball collision

A stationary billiard ball, mass 0.17 kg, is struck by an identical ball moving at 4.1 m/s. After the collision, the second ball moves off at 60° to the left of its original direction. The stationary ball moves off at 30° to the right of the moving ball's original direction. What is the speed of each ball after the collision?

Physics: Momentum and Speed

Question: A 5.00 g bullet is fired with a velocity of 109.5 m/s toward a 8.35 kg stationary solid block resting on a friction less surface. (a) What is the change in momentum of the bullet if it is embedded in the block? (b) What is the change in momentum of the bullet if it ricochets in the opposite direction with a spee

Collision of hammer and nail

The collision between a hammer and a nail can be considered to be approximately elastic. Estimate the kinetic energy acquired by a 14.4 g nail when it is struck by a 572 g hammer moving with a speed of 4.61 m/s.

Magnetic Effects of Current

If a wire is placed next to the face of a permanent magnet and a current sent through the wire, then a Lorentz force is present orthogonal to both the direction of the current and the magnetic field. I would assume there should be a linear force on the magnet in the other direction, but the magnetic field caused by the current i

Collision: No jerk experienced by a passengers of a bus

You are a professional witness in a lawsuit. What do you tell the judge? and Why? Explain and use equations Scenario: You are on an RTD Stretch Bus (the long busses with the accordion in the middle. (This is called an articulating bus.)) The bus is fully loaded with fuel and people. You are traveling at 30 [mph] when a mi

Mechanics: Collision, conservation of momentum.

After sliding down a snow covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of +2.7 m/s. Miranda runs after her at a velocity of +45 m/s and hops on the inner tube. How fast do the two of them slide across the snow together on the inner tube? Ashleys mass is 71 kg and Mirandas is 5

Glancing collision of two pucks

A puck of mass 80.0 g and radius 3.60 cm slides along an air table at a speed of 1.50 m/s as shown in Figure P11.34a. It makes a glancing collision with a second puck of radius 6.00 cm and mass 125.0 g (initially at rest) such that their rims just touch. Because their rims are coated with instant-acting glue, the pucks stick tog

Collision of two balls

Please help with the following solution. A softball of mass 0.221 kg that is moving with a speed of 6.5 m/s (in the positive direction) collides head-on and elastically with another ball initially at rest. Afterward it is found that the incoming ball has bounced backward with a speed of 4.3 m/s. (a) Calculate the velocity

The momentum of collisions worksheet

A 10000kg semi truck traveling at 15 m /s loses its brakes as it approaches a stop sign. A small car sitting at the stop sign is hit by the truck and travels into the intersection at 14.4 m/s. What is the mass of the small car?

Collision in the Lab frame

An experiment is to be designed to measure the differential cross section for elastic pion-proton scattering at a CM (center of mass) scattering angle of 70 degrees and a pion CM kinetic energy of 490KeV Find teh angles in the lab at which the scattered pions, and recoiling protons should be detected, and teh required Lab kinet

Conservation of Momentum: Amount of Mass Expelled

A rocket of total mass 3180 kg is traveling in outer space with a velocity of 115 m/s toward the Sun. It wishes to alter its course by 33.0°, and can do this by firing its rockets briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1760 m/s, how much mass must be expelled?

Spinning satellites

Hello, I have the following problem: A zero-momentum spinner has a momentum wheel spinning at 5000 rpm. The angular momentum of the wheel is 100 N-m-s. a) What is the spin rate of the spacecraft if its moment of inertia, Is = 500 kg-m2? b) What is the moment of inertia of the wheel? c) If the wheel suddenly stops, wh

The Momentum of a Photon and the Compton Effect

An incident X-ray photon of wavelength 0.2800 nm is scattered from an electron that is initially at rest. The photon is scattered at an angle of theta = 180.0° (in picture) and has a wavelength of 0.2839 nm. Use the conservation of linear momentum to find the momentum gained by the electron. (answer in kg*m/s)