Exam 9: Center of Mass and Linear Momentum

Sphere A has mass m and is moving with velocity v.It makes a head-on elastic collision with a stationary sphere B of mass 2m.After the collision their speeds (v_A, v_B)are:

Two 4.0-kg blocks are tied together with a compressed spring between them.They are thrown from the ground with an initial velocity of 35 m/s, 45° above the horizontal.At the highest point of the trajectory they become untied and spring apart.About how far below the highest point is the center of mass of the two-block system 2.0 s later, before either fragment has hit the ground?

The plot shows the force acting on an object as a function of time.Over the time the force is applied, the total impulse is:

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 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:

A 25-kg box of books is dropped on the floor from a height of 1.1 m and comes to rest.What impulse did the floor exert on the box?

Block A, with a mass of 4.0 kg, is moving with a speed of 2.0 m/s while block B, with a mass of 8.0 kg, is moving in the opposite direction with a speed of 3.0 m/s.The center of mass of the two-block system is moving with the velocity of:

A 2.0-kg mass is attached to one end of a spring with a spring constant of 100 N/m and a 4.0-kg mass is attached to the other end.The masses are placed on a horizontal surface and the spring is compressed 10 cm.The spring is then released with the masses at rest and the masses oscillate.When the spring has its equilibrium length for the first time the 2.0-kg mass has a speed of 0.36 m/s.The mechanical energy that has been lost to this instant is:

A shell is launched from a cannon and explodes mid-air.Which of the following is correct after the explosion?

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?

If the total momentum of a system is changing:

The x and y coordinates in meters of the center of mass of the three-particle system shown below are:

A uniform narrow bar, resting on frictionless ice, is given a transverse horizontal impulse at one end as shown.The center of mass of the bar COM will then:

Whenever an object strikes a stationary object of equal mass:

Two bodies of unequal mass, placed at rest on a frictionless surface, are acted on by equal horizontal forces for equal times.Just after these forces are removed, the body of greater mass will have:

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

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 640-N hunter gets a rope around a 3200-N polar bear.They are stationary, 20 m apart, on frictionless level ice.When the hunter pulls the polar bear to him, the polar bear will move:

A ball hits a wall and rebounds with the same speed, as diagrammed below.The changes in the components of the momentum of the ball are:

A 5-kg object can move along the x axis.It is subjected to a force in the positive x direction; a graph of F as a function of time t is shown below.Over the time the force is applied the change in the velocity of the object is: