Exam 8: Systems of Particles and Conservation of Linear Momentum

Two objects,one of mass m₁ = 2 kg and the second of unknown mass,are connected by a compressed spring with negligible mass.The system is at rest on a frictionless table.Both objects are released simultaneously.m₁ is observed to recoil with velocity v₁ = 2 m/s ,and m₂ shots forward with velocity v₂ = 4 m/s .What is the mass of m₂?

A toy car of mass 2.0 kg moving to the right with a speed of 8.0 m/s collides perfectly inelastically with another toy car of mass 3.0 kg that is moving to the left with a speed of 2.0 m/s.Immediately after the collision the velocity of the system is

The force exerted on a 10-kg mass is given by where the units are SI.If the mass starts from rest,its velocity after 2 s is

A helium atom (mass = 4m)moving with speed V collides elastically with a tritium (hydrogen 3 )atom (mass = 3m)at rest.Calculate the speed of the tritium atom after the collision.

A particle with speed v₁ = 2.64 $\times$ 10⁶ m/s makes a glancing elastic collision with another particle that is at rest.Both particles have the same mass.After the collision,the struck particle moves off at 45º to v₁.The speed of the struck particle after the collision is approximately

Two students,sitting on frictionless carts,push against each other.Both are initially at rest and the mass of student 1 and the cart is M,and that of student 2 and the cart is 1.5M.If student 1 pushes student 2 so that she recoils with velocity ,what is the change in momentum of the two students?

A railway car having a total mass of 5.8 $\times$ 10⁵ kg,moving with a speed of 9.1 km/h,strikes another car that has a mass of 8.7 $\times$ 10⁵ kg and is initially at rest.The speed of the coupled cars after the collision is

Two particles,m₁ and m₂,each with mass m,is moving with velocity and respectively.The momentum of m₁ relative to the center-of-mass is

Two particles,each of mass m,are moving with velocity and The kinetic energy at the center-of-mass is

A bullet is fired at 100 m/s horizontally into a 2-kg block suspended by a light string of length 1.2 m.If the block and bullet system swing up by 20 degrees to the vertical,the mass of the bullet is given by:

A projectile with a mass 6M is fired at a speed of 400 m/s at an angle of 60º above the horizontal.At the highest point of its trajectory,the projectile is broken into two equal pieces by an internal explosion.Just after the explosion,one of the two pieces is known to be traveling vertically downward at a speed of 300 m/s.The magnitude of the velocity of the other half of the projectile is

A 5.0-kg ball and a 10.0-kg ball approach each other with equal speeds of 20 m/s.If they collide inelastically,the speed of the balls just after the collision is approximately

A 20-g bullet with an initial velocity of 3.0 $\times$ 10⁴ cm/s penetrates 6.0 cm into a stationary wall.The average force exerted on the bullet by the wall in bringing it to rest is approximately

Use the scenario below for the next question. You were traveling north at speed vc in your car of mass m_c = 2000 kg through an intersection when you were struck by a light truck of mass m_t = 4000 kg traveling West. After the collision the two vehicles are stuck together and travel a distance of 20 m in the direction 30° N of W. -If your speed is 72 km/h,what is the work done by friction in bringing the two vehicles to rest after the collision?

A pitcher throws a baseball with a velocity of 27 m/s.After being struck by a bat the ball travels in the opposite direction with a velocity of 40 m/s.If the ball has a mass of 0.11 kg and is in contact with the bat for 3.0 ms,the average force exerted by the bat on the ball is

A force acting on an object is approximated as F = 4 sin (100 $\pi$ t)N from t = 0 to t = 10 ms.Calculate the impulse on the object.

A moving particle is stopped by a single head-on collision with a second,stationary particle if the moving particle undergoes

For this question,assume that all velocities are horizontal and that there is no friction.Two skaters A and B are on an ice surface.A and B have the same mass M = 90.5 kg.A throws a ball with mass m = 200 g toward B with a speed v = 21.5 m/s relative to the ice.B catches the ball and throws it back to A with the same speed.After A catches the ball,his speed with respect to the ice is

Two billiard balls are traveling to the right with speeds v₁ = +0.5 m/s and v₂ = +0.3 m/s.If m₁ = 2.5m₂,calculate the velocity of m₁ after it catches up to and impacts m₂.The speed of m₂ after the collision is +0.55 m/s.

A particle of unknown mass has a momentum of 73 kg · m/s.At a time 7.3 s later,the momentum of the particle is 38 kg · m/s.What is the magnitude of the force acting on the particle during the interval,assuming the motion is in a straight line?