Exam 8: Momentum and Collisions

A 4.0-kg mass,initially at rest on a horizontal frictionless surface,is struck by a 2.0-kg mass moving along the x axis with a speed of 8.0 m/s.After the collision,the 2.0-kg mass has a speed of 4.0 m/s at an angle of 37 $\degree$ from the positive x axis.What is the speed of the 4.0-kg mass after the collision?

Exhibit 9-1 Use this exhibit to answer the following question. Two birds of prey hurtling after the same mouse collide in mid-air and grab each other with their talons.Each 250-g bird is flying at 30 m/s at a 60 $\degree$ angle to the ground. -Refer to Exhibit 9-1.What is the magnitude of their velocity,in m/s,immediately after the collision?

If you know the impulse that has acted on a body of mass m you can calculate

A child bounces a 50-gram superball on the sidewalk.The velocity of the superball changes from 21 m/s downward to 19 m/s upward.If the contact time with the sidewalk is 1/800 s,what is the magnitude of the force exerted on the superball by the sidewalk?

At an instant when a particle of mass 50 g has an acceleration of 80 m/s² in the positive x direction,a 75-g particle has an acceleration of 40 m/s² in the positive y direction.What is the magnitude of the acceleration of the center of mass of this two-particle system at this instant?

Two boys in a canoe toss a baseball back and forth.What effect will this have on the canoe? Neglect (velocity-dependent)frictional forces with water or air.

A 6.0-kg object,initially at rest in free space,"explodes" into three segments of equal mass.Two of these segments are observed to be moving with equal speeds of 20 m/s with an angle of 60 $\degree$ between their directions of motion.How much kinetic energy is released in this explosion?

The linear density of a rod,in g/m,is given by $\lambda = 40.0 + 30.0 x$ .The rod extends from the origin to x = 0.400 m.What is the location of the center of mass of the rod?

A 10-g bullet moving horizontally with a speed of 2.0 km/s strikes and passes through a 4.0-kg block moving with a speed of 4.2 m/s in the opposite direction on a horizontal frictionless surface.If the block is brought to rest by the collision,what is the kinetic energy of the bullet as it emerges from the block?

In an elastic collision between two bodies of mass m₁ and m₂,with m₂ initially at rest,mass 1 moves off at angle $\theta$ relative to the direction of its initial velocity and mass 2 at angle $\phi$ .An exam paper shows the equations below: m₁v_1i 0 = m₁v_1f cos $\theta$ + m₂v_2f sin $\phi$ = m₁v_1f sin $\theta$ + m₂v_2f cos $\phi$ What error(s)has the student made?

A 2.0-kg object moving 3.0 m/s strikes a 1.0-kg object initially at rest.Immediately after the collision,the 2.0-kg object has a velocity of 1.5 m/s directed 30 $\degree$ from its initial direction of motion.What is the x component of the velocity of the 1.0-kg object just after the collision?

Three particles are placed in the xy plane.A 40-g particle is located at (3,4)m,and a 50-g particle is positioned at (-2,-6)m.Where must a 20-g particle be placed so that the center of mass of this three-particle system is located at the origin?

An exam paper contains the following equation for rocket propulsion: $( M + \Delta m ) v = M ( v + \Delta v ) + \Delta m \left( v + v _ { e } \right)$ . The error in the equation is that,instead of (v + v_e),the velocity of the fuel relative to the ground should be

A U-238 nucleus (mass = 238 units)decays,transforming into an alpha particle (mass = 4.00 units)and a residual thorium nucleus (mass = 234 units).If the uranium nucleus was at rest,and the alpha particle has a speed of 1.50 * 10⁷ m/s,determine the recoil speed of the thorium nucleus.

The only force acting on a 2.0-kg object moving along the x axis is shown.If the velocity v_x is +2.0 m/s at t = 0,what is the velocity at t = 4.0 s?

A ball falls to the ground from height h and bounces to height h'.Momentum is conserved in the ball-earth system

A 3.0-kg mass is sliding on a horizontal frictionless surface with a speed of 3.0 m/s when it collides with a 1.0-kg mass initially at rest as shown in the figure.The masses stick together and slide up a frictionless circular track of radius 0.40 m.To what maximum height,h,above the horizontal surface will the masses slide?

A rocket with an initial mass of 1 000 kg adjusts its thrust by varying the rate at which mass is ejected.The ejection speed relative to the rocket is 40 km/s.If the acceleration of the rocket is to have a magnitude of 20 m/s² at an instant when its mass is 80% of the original mass,at what rate is mass being ejected at that instant? Ignore any external forces on the rocket.

Two bodies with masses m₁ and m₂ are both moving east with velocities of magnitudes v₁ and v₂,where v₁ is less than v₂.The magnitude of the velocity of the center of mass of this system of two bodies is

A 2.4-kg ball falling vertically hits the floor with a speed of 2.5 m/s and rebounds with a speed of 1.5 m/s.What is the magnitude of the impulse exerted on the ball by the floor?