Exam 9: Center of Mass and Linear Momentum

Two boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod.The boys pull themselves together along the rod.When they meet the 40-kg boy will have moved what distance?

A 2.5-kg stone is released from rest and falls toward Earth.After 4.0 s, the magnitude of its momentum is:

A 0.3 kg rubber ball is dropped from the window of a building.It strikes the sidewalk below at 30 m/s and rebounds up at 20 m/s.The magnitude of the impulse due to the collision with the sidewalk is:

The center of mass of the system consisting of Earth, the Sun, and the planet Mars is:

A hockey puck of mass m traveling along the x axis at 4.5 m/s hits another identical hockey puck at rest.If after the collision the second puck travels at a speed of 3.5 m/s at an angle of 30° above the x axis, is this an elastic collision?

A projectile in flight explodes into several fragments.The total momentum of the fragments immediately after this explosion:

The center of mass of a uniform disk of radius R is located:

If a projectile hits a stationary target, and the projectile stops while the target moves at the same speed as the incoming speed of the projectile,

A thick uniform wire is bent into the shape of the letter "U" as shown.Which point indicates the location of the center of mass of this wire?

A stream of gas consists of n molecules.Each molecule has mass m and speed v.The stream is reflected elastically from a rigid surface as shown.The magnitude of the change in the total momentum of the stream is:

An inelastic collision is one in which:

A 3.00-g bullet traveling horizontally at 400 m/s hits a 3.00-kg wooden block, which is initially at rest on a smooth horizontal table.The bullet buries itself in the block without passing through.The speed of the block after the collision is:

A machinist starts with three identical square plates but cuts one corner from one of them, two corners from the second, and three corners from the third.Rank the three plates according to the x coordinates of their centers of mass, from smallest to largest.

A 3-g bullet is fired horizontally into a 10-kg block of wood suspended by a rope from the ceiling.The block swings in an arc, rising 3 mm above its lowest position.The velocity of the bullet was:

A cart loaded with sand slides forward along a horizontal frictionless track.As the cart moves, sand trickles out at a constant rate through a hole in the back of the cart.The acceleration of the cart is:

A 500-kg sack of coal is dropped on a 2000-kg railroad flatcar which was initially moving at 3 m/s as shown.After the sack rests on the flatcar, the speed of the flatcar is:

Sphere X, of mass 2 kg, is moving to the right at 10 m/s.Sphere Y, of mass 4 kg, is moving to the left at 10 m/s.The two spheres collide head-on.The magnitude of the impulse of X on Y is:

If a projectile hits a stationary target, and the projectile rebounds and travels back the way it came,

The acceleration of the center of mass of a system of particles changes as a = 4.5t + 2.4t² + 1.1t³, where a is in m/s².If the system starts from rest at t = 0, what is its velocity at t = 2.0 s?

The velocity of the center of mass of a system of particles changes as v = 4.5 t + 2.4 t² + 1.1 t³, where v is in meters per second.If the system starts from rest at t = 0, what is its position at t = 3.0 s?