Unit 9: Linear Momentum and Collisions
Impulse, collisions replayed head-on and at angles, center of mass, and the rocket equation's variable-mass twist on momentum.
8 topics · 30 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Momentum and Impulse
- How it worksHow does impulse, the product of force and the time it acts, change an object's momentum?
- Worked exampleFind the impulse delivered to a 0.15 kg ball that changes velocity from 20 m/s to -15 m/s off a bat.
- Common mistakeWhy isn't momentum the same thing as kinetic energy, even though both involve mass and velocity?
Your turn1 of 2
A 0.379 kg ball hits a bat, changing its velocity from 23 m/s to -6 m/s (it reverses direction; positive is the ball's original direction). What is the impulse delivered to it, in newton-seconds?The Impulse-Momentum Theorem
- How it worksHow does stretching out the time of a collision reduce the average force for the same total impulse?
- Worked exampleFind the average force on a 60 kg crash test dummy that stops from 15 m/s in 0.1 seconds.
- Going furtherWhat happens to the force felt in a collision if the stopping time is stretched from 0.1 s to 1 s?
Your turn1 of 2
A 75 kg crash test dummy moving at 20 m/s comes to a stop in 0.283 s. What is the average force on it, in newtons?Conservation of Momentum
- How it worksHow does Newton's third law guarantee that total momentum stays constant when only internal forces act?
- Worked exampleFind the recoil velocity of a 5 kg cannon that fires a 0.1 kg ball at 100 m/s.
- Common mistakeWhy doesn't conservation of momentum require the two objects involved to have equal masses or equal speeds?
Your turn1 of 2
A 8 kg cannon, initially at rest, fires a 0.212 kg ball at 143 m/s. What is the recoil speed of the cannon, in meters per second?Elastic Collisions in One Dimension
- How it worksHow do conservation of momentum and conservation of kinetic energy together pin down both final velocities?
- Worked exampleFind the final velocities of a 2 kg ball moving at 6 m/s that elastically collides head-on with a stationary 2 kg ball.
- Common mistakeWhy doesn't an elastic collision mean that the two objects stick together afterward?
- Going furtherWhat happens to the final velocities in an elastic collision when the target mass is much larger than the incoming one?
Your turn1 of 2
A 4 kg ball moving at 10 m/s collides head-on, elastically, with a stationary 4 kg ball. What is the velocity of the first ball immediately after the collision, in meters per second (positive means it continues in its original direction)?Inelastic and Perfectly Inelastic Collisions
- How it worksHow does momentum stay conserved in an inelastic collision even while kinetic energy does not?
- Worked exampleFind the common final velocity after a 1000 kg car moving at 20 m/s collides and sticks with a stationary 1500 kg car.
- Common mistakeWhy doesn't losing kinetic energy in a collision mean that momentum is lost too?
- Going furtherWhat happens to the fraction of kinetic energy lost in a collision as the two colliding masses become more unequal?
Your turn1 of 2
A 1287 kg car moving at 20 m/s collides and sticks with a stationary 1925 kg car. What is their common velocity immediately after, in meters per second?Collisions in Two Dimensions
- How it worksHow do you apply momentum conservation separately along the x-axis and the y-axis for a 2D collision?
- Worked exampleFind the final velocity components of a 3 kg ball moving at 5 m/s that strikes an identical stationary ball and deflects 40 degrees.
- Common mistakeWhy doesn't momentum conservation in two dimensions mean the total speed of the objects has to stay the same?
- Going furtherWhat happens to the angle between two equal-mass billiard balls after an elastic, off-center collision?
Your turn1 of 2
A puck moving at 10 m/s strikes an identical stationary puck in an elastic, off-center collision. For equal masses in an elastic collision, the two final velocities are always perpendicular to each other. If the originally moving puck deflects by 52 degrees from its original direction, what is its speed immediately after the collision, in meters per second?Center of Mass
- How it worksHow do you find the center of mass of a system by weighting each piece's position by its mass?
- Worked exampleFind the center of mass of a 2 kg object at x = 0 m and a 3 kg object at x = 5 m.
- Worked exampleFind the center of mass of three particles: 2 kg at x = 0, 3 kg at x = 2 m, and 5 kg at x = 6 m.
- Common mistakeWhy doesn't the center of mass of an object have to be located inside the object's own material?
- Going furtherWhat happens to the motion of a system's center of mass when an internal explosion sends its pieces flying apart?
Your turn1 of 2
Three particles lie on the x-axis: 3 kg at x = 0 m, 4 kg at x = 4 m, and 3 kg at x = 5 m. What is the x-coordinate of their center of mass, in meters?Variable-Mass Systems and the Rocket Equation
- How it worksHow does a rocket use conservation of momentum on itself and its expelled exhaust to gain speed?
- Worked exampleFind the change in velocity of a rocket that starts at 10000 kg, ends at 4000 kg, and expels exhaust at 3000 m/s.
- Common mistakeWhy doesn't a rocket need air or anything else outside it to push against in order to accelerate?
- Ties togetherHow does the rocket equation reduce to ordinary momentum conservation for one single instant of fuel burn?
Your turn1 of 2
A rocket starts with mass 12875 kg, ends with mass 4947 kg after burning fuel, and expels exhaust at 3864 m/s relative to itself. Using the Tsiolkovsky rocket equation, what is its change in velocity, in meters per second?