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Conservation of Momentum

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Wize University Physics Textbook (Master) > Momentum, Impulse and Collisions

Conservation of Linear Momentum

5 Activities

Wize University Physics Textbook (Master) > Momentum, Impulse and Collisions

Collisions

7 Activities

One pool ball of mass 1 kg traveling with a velocity of 5 m/s hits another ball of mass 2 kg moving towards it at 4 m/s. The collision is head on and elastic. Find the final velocities of both balls after the collision.
More Conservation of Linear Momentum Questions:
Pendulum knocking into a mass
Two masses are hanging off the same point on a beam, both with a 1.0m long string, shown in the diagram. Mass 1 is 5.1kg while mass 2 is 3.9kg.
Mass 1 is lifted up an angle of 33.0o from the vertical, and released. Ignore all friction and drag forces.
A 15.0 kg ball is fired from a 3000.0 kg cannon. The cannon is on a rail that only allows it to move in the horizontal direction. The ball is fired at 480.0 m/s at 20.0o above the +x axis. What is the speed of the cannon? Let +x be to the right, and +y be upward, give your answer in m/s.
Momentum: Collision
Two carts on a friction less surface collide and stick to each other. What is the velocity of the two carts after collision?
A 200g mass block is released from rest at a height of 25 cm on 30o incline. The incline is frictionless. It slides down the incline and then a frictionless surface until it collides elastically with an 800g block at rest 1.4 m from the bottom of the incline as shown in the figure. How much later do the two blocks collide again?
A ball of mass 0.5 kg is attached to a string of length 26 cm. The ball is raised so that the string is taut and horizontal. Now the ball is released such that it swings and undergoes an elastic head-on collision with a stationary ball of mass 0.20kg that is free to roll horizontally. a) Find the speed of the swinging ball just before the collision. b) What is the speed of the 0.20 kg ball just after the collision?
A car accidentally enters a playing ground at a velocity of 14m/s. A child tosses a ball at the car at 18m/s. What is the ball's speed after it rebounds elastically from the car?
A ballistic pendulum is used to measure the speed of a bullet. It consists of a wooden block of mass M = 10kg suspended from a vertical string. A bullet of mass m = 100g strikes and embeds itself in the block and the block swings upward through a vertical distance of 0.10m. What is the bullet's speed?
A 12 g bullet moving horizontally at 30 m/s is fired into a vertically suspended pendulum of mass 2.5 kg. The bullet becomes embedded in the pendulum.
A 4.0 kg ball with a velocity of 3.0 m/s at 45º to the horizontal collides in an elastic collision with a 3.5 kg ball initially at rest. The 4.0kg ball moves off at 2.0 m/s at 30º to the horizontal. What is the final velocity of the 3.5 kg ball?
As shown below, a ball of mass m with an initial velocity 10 m/s collides with an initially stationary ballistic pendulum of mass M=3m, hanging from a string. The two sticks together and system deflects from vertical position to angleΘ=60∘\Theta=60^{^{\circ}} What is the length of string?
The expending gases that leave the muzzle of a rifle also contribute to the recoil.A .30-caliber bullet has mass 0.0072 kg and a speed of 601 m/s relative to the muzzle when fired a rifle that has mass 2.80 kg.The loosely held rifle recoils at a speed of 1.85 m/s relative to the earth.Find the momentum of the propellant gases in a coordinate system attached to the earth as they leave the muzzle of the rifle.
Conservation of Energy & Momentum
A 12-g rifle bullet is fired with a speed of 380 m/s into a ballistic pendulum with mass 6.00 kg, suspended from a cord 70.0 cm long. Compute (a) the vertical height through which the pendulum rises , (b) the initial kinetic energy of the bullet, and (c) the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the pendulum.
A 15.0-kg block is attached to a very light horizontal spring of force constant 500 N/m and is resting on a friction-less horizontal table (Fig.). Suddenly it is struck by a 3.00-kg stone traveling horizontally at 8.00 m/s to the right, where upon the stone rebound at 2.00 m/s horizontally to the left.Find the maximum distance that the block will compress the spring after the collision.
A 5 kg chunk of ice is sliding at 12.0 m/s on the floor of an ice-covered valley when it collides with and stick to another 5.00-kg chunk of ice that is initially at rest.(Fig.) Since the valley is icy, there is no friction.After the collision, how high above the valley floor will the combined chunks go?
A 0.15 kg frame, when suspended from a coil spring, stretches the spring 0.070 m.A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm(Fig). Find the maximum distance the frame moves downward from its initial position.
Two identical masses are released from rest in a smooth hemispherical bowl of radius R from the positions shown in Fig. You can ignore friction between the masses and the surface of bowl. If they stick together when they collide, how high above the bottom of the bowl will the masses go after colliding in terms of R?
More Collisions Questions:
Problem Set-Momentum
Practice: 2D Linear Momentum Conservation
You throw a 5 kg ball directly eastward at 6 m/s toward a stationary 4 kg ball.  After colliding, the 5 kg ball is deflected 45° north of the horizontal at a speed of 2 m/s.  What is the speed and direction of the 4 kg ball after collision? Is this collision elastic?
Perfectly inelastic car crash
Practice: 2D Inelastic Collision
Two cars collide at an intersection. Car A, with a mass of 2000.0 Kg, is going from west to east, while car B, of mass 1500 kg, is going from north to south at 15 m/s. As a result of this collision, the two cars become mushed and move as one afterward. In your role as an expert witness, you inspect the scene and determine that, after the collision,the enmeshed cars moved at an angle of 65∘ 65^{\circ}\ south of east from the point of impact.
(a) How fast were the enmeshed cars moving just after the collision?
Practice: 1D Collision
A ball of mass 0.500kg moving at 4.00m/s hits a stationary ball of mass 3.50kg. Assume no friction in this system and the collision is elastic, what are the final velocities of the two balls?
Kinematics: Momentum
One pool ball of mass 14.0 grams traveling with a velocity of 5 m/s (Ball A) hits another ball of mass 23.0 grams moving at 3.4 m/s (Ball B). The collision is head-on and elastic. Find the final speeds of both balls after the collision.
Practice: Car crash (inelastic)
Two cars collide at an intersection. Car A, with a mass of 2000 Kg, is going from west to east, while car B, of mass 1500 kg, is going from north to south at 15 m/s. As a result of this collision, the two cars become enmeshed and move as one afterward.In your role as an expert witness, you inspect the scene and determine that, after the collision,the enmeshed cars moved at an angle of 65∘ 65^{\circ}\ south of east from the point of impact.
Momentum and spring
A 15.0-kg block is attached to a very light horizontal spring with spring constant 500 N/m and is resting on a friction-less horizontal table. It is struck by a 3.00-kg stone traveling horizontally at 8.00 m/s to the right. The stone rebounds at 2.00 m/s horizontally to the left. Find the maximum distance that the block will compress the spring after the collision.
Momentum: Colliding balls
You throw a 5 kg ball directly eastward at 6 m/s toward a stationary 4 kg ball.  After colliding, the 5 kg ball is deflected 40° north of the horizontal at a speed of 2 m/s.
Kinematics and Simple Harmonic Motion
A 12 g bullet moving horizontally at 30 m/s is fired into a hanging mass of 2.5 kg. The bullet becomes embedded in the hanging mass, which then acts like a pendulum. The cord connecting the mass to the ceiling is 75.0 centimeters.
Kinematics: Momentum
A bowling ball (mass 5.0kg) travelling at 0.75 m/s hits a bowling pin (mass 1.6kg), initially at rest. The bowling pin moves off with a speed of 1.25 m/s at an angle of 35º relative to the initial direction of the bowling ball. What is the final velocity of the bowling ball?
(Important hint: You cannot assume the collision is elastic.).
Select a magnitude and a direction from the options below.
Kinematics: Momentum
Particle m1 with mass of4×10−25 kg4\times 10^{-25}~\rm kgis travelling with a velocity of 5msı^5\frac{m}s\hat\imath , and collides with particle m2 with mass 6×10−25 kg6\times 10^{-25}~\rm kg which is initially at rest. After the interaction, m1 travels with a speed of 5 m/s, deflected by an angle of 45 degrees relative to its initial path.
a) What is the total momentum of the system?
b) What is the velocity of m2 after the collision?
Conservation of Momentum
A car accidentally enters a playground at a velocity of 14m/s. A child tosses a ball at the car at 18m/s. What is the ball's speed after it rebounds elastically from the car? (Assume it's a head-on collision.)
Momentum: Swinging ball hits another ball
A ball of mass 0.50 kg is attached to a string of length 26 cm. The ball is raised so that the string is taut and horizontal. Now the ball is released such that it swings and undergoes an elastic head-on collision with a stationary ball of mass 0.20kg that is free to roll horizontally. The mass strikes the ball when the string is vertical (that is, it falls through a full 90 degrees before hitting the ball).
Kinematics: Radioactive decay and momentum
A radioactive atom at rest with a mass of 100×10−27 kg100\times 10^{-27}~kgundergoes decay to three particles with masses of 25×10−27 kg25\times 10^{-27}~kg , 40×10−27 kg40\times 10^{-27}~kg and 35×10−27 kg35\times 10^{-27}~kg respectively. Assume that all three particles remain in the x-y plane.
If the first particle is moving in the direction of positive y axis at speed of 20m/s and the second particle moves in the direction of 25 degree clockwise respect to positive x-axis at speed of 15 m/s, what is the angle and speed of the of the third particle?
(Note: if you are wondering why the masses don't add up, it's because of special relativity and mass-energy equivalence. Something to Google if you're interested. If these were anything other than atomic nuclei, though, you should expect the masses to add up properly.)
Collision practice
A 4.0 kg ball with a velocity of 3.0 m/s at 45º to the horizontal collides in an elastic collision with a 3.5 kg ball initially at rest. The 4.0kg ball moves off at 2.0 m/s at 30º to the horizontal. What is the final velocity of the 3.5 kg ball?
Dropping a big and small ball
Two balls are dropped from rest, with one directly above the other. The lower ball has a mass 10 times that of the higher ball. Assume that all collisions between the balls and with the floor are elastic. How high will each ball rebound, compared to the initial drop height h?
Practice: BMW and truck collision
A 1200-kg BMW and a 2200-kg truck collide at a right angle in an airport crossing. They skid together for 22m; the coefficient of friction is 0.91. Show that at least one car must have exceeded the 25 km/h speed limit at the intersection.
Slide and collide
A 5.00kg box is sliding down a 20.0m tall slide that makes an angle of 60.0o with the ground. The coefficient of friction for the slide is 0.750.
At the bottom of the slide it slides on a frictionless surface and collides with a 2.50kg stationary mass.
A 5 kg chunk of ice is sliding at 12.0 m/s on the floor of an ice-covered valley when it collides with and stick to another 5.00-kg chunk of ice that is initially at rest. Since the valley is icy, there is no friction. After the collision, how high above the valley floor will the combined chunks go?
Match the terms.
A ball of mass 0.500kg moving at 4.00m/s hits a stationary ball of mass 3.50kg. Assume no friction in this system, what are the final velocities of the two balls?
Problem Set-Momentum
You throw a 5 kg ball directly eastward at 6 m/s toward a stationary 4 kg ball.  After colliding, the 5 kg ball is deflected 45° north of the horizontal at a speed of 2 m/s.  What is the speed and direction of the 4 kg ball after collision? Is this collision elastic?
Perfectly inelastic car crash
Two cars collide at an intersection. Car A, with a mass of 2000.0 Kg, is going from west to east, while car B, of mass 1500 kg, is going from north to south at 15 m/s. As a result of this collision, the two cars become mushed and move as one afterward. In your role as an expert witness, you inspect the scene and determine that, after the collision,the enmeshed cars moved at an angle of 65∘ 65^{\circ}\ south of east from the point of impact.
(a) How fast were the enmeshed cars moving just after the collision?
(b) How fast was car A going just before the collision?
Particle m1 with mass of 4kg is travelling with a velocity of 5msı^5\frac{m}s\hat\imath , and collides with particle m2 with mass 6×10−25 kg6\times 10^{-25}~\rm kg which is initially at rest. After the interaction, m1 travels with speed of 5 m/s at an angle of 45 degrees with vector.
What is the total momentum of the system?
What is the vector velocity of m2?
Momentum: Collision
Two carts on a friction less surface collide and stick to each other. What is the velocity of the two carts after collision?
A 1200-kg BMW and a 2200-kg truck collide at right angles in an airport crossing. They skid together for 22m; the coefficient of friction is 0.91. Show that at least one car must have exceeded the 25 km/h speed limit at the intersection.
Conservation of Energy & Momentum
A 12-g rifle bullet is fired with a speed of 380 m/s into a ballistic pendulum with mass 6.00 kg, suspended from a cord 70.0 cm long. Compute (a) the vertical height through which the pendulum rises , (b) the initial kinetic energy of the bullet, and (c) the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the pendulum.