Exam 8: Systems of Particles and Extended Objects

A system consists of two particles: particle 1,having the mass m₁ = 4.0 kg is located at (-4.0 m,1.0 m)and particle 2,having the mass m₂ = 5.0 kg is located at (2.0 m,1.0 m).The direction of the position vector of the center of mass of the system measured from the positive x-axis is

A 1900-kg cannon shoots a 5-kg cannon ball at a velocity of 25 m/s.What is the recoil velocity of the cannon?

An explosive hockey puck of mass 0.127 kg slides along the ice at 32 m/s in the +x direction,and explodes,leaving a 0.075-kg chunk stationary.What is the speed of the other chunk?

A long thin rod has its one end at x = 0 and the other end at x = 2 m.Its composition is such that the linear mass density changes with length according to $\lambda$ (x)= ax² + bx+c,where x is the distance from one end of the rod.Given: a = 0.75 kg/m³,b = 0.5 kg/m²,and c = .25 kg/m,the mass of the rod is

A large number N of small identical stones are all located on the positive x-axis.The first is located at x = 1 m,the second at x = 3 m,the third at x = 5 m,and so on.The x-coordinates of all of the stones measured in meters are odd numbers.Where is their center of mass located?

A ping pong ball has a mass of 2.47 g,a diameter of 4.0 cm and is made of celluloid.( )Find the thickness of the celluloid.

A rocket explodes into three pieces of equal mass.Immediately after the explosion their velocities are (120 m/s,south),(240 m/s,north)and (120 m/s east).What was the velocity of the rocket's center of mass before the explosion?

A circular pizza of radius R has a circular piece of radius removed from one side,as shown in the figure.The center of mass of the pizza with the hole is at a distance of R/6 from the center of mass of the original pizza.The radius of the circular piece removed is

In the water molecule,the hydrogen and oxygen atoms are separated by 10^-10 m and the bond angle between the two hydrogen-oxygen bonds is 105 ^$\circ$ .the mass of the hydrogen atom is 1 u and that of the oxygen atom is 16 u.The center of mass of the water molecule along the line of symmetry from the oxygen atom is

A toy car of mass 4.0 kg is sitting stationary when a child rolls a toy truck of mass 6.5 kg straight towards it in the negative x-direction with a speed of 5.0 m/s.The velocity of the center of mass of the system consisting of the two toys is

A 25-kg boy jumps off of a 100-kg raft.If the boy jumps off at a speed of 4.90 m/s relative to the lake,what is the speed of the raft relative to the boy? Ignore the effects of water resistance.

In the water molecule,the hydrogen and oxygen atoms are separated by 10^-10 m and the bond angle between the two hydrogen-oxygen bonds is 105 ^$\circ$ .the mass of the hydrogen atom is 1 u and that of the oxygen atom is 16 u.The center of mass of the water molecule along the line of symmetry from the oxygen atom is

A system consists of two particles: particle 1,having the mass m₁ = 2.0 kg has the velocity, and particle having the mass m₂ = 5.0 kg has the velocity, The magnitude of the velocity of the center of mass of the system is

Suppose we have a rocket in outer space.The rocket consists of a payload of 5280.0 kg and 130300.0 kg of fuel.Assume that the rocket starts from rest,accelerates to its final velocity.After reaching this final velocity it begins its 3.82 * 10⁵ km trip to the moon.What is the speed at which we must expel the propellant to make the trip from the Earth to the Moon,a distance of 3.82 * 10⁵ km,in 7.5 hours? (in km/s)

Suppose we have a rocket in outer space.The rocket consists of a payload of 5280.0 kg.Assume that the rocket starts from rest,accelerates to its final velocity.After reaching this final velocity it begins its 3.82 * 10⁵ km trip to the moon.The speed at which the rocket expels propellant is 5.11 km/s.If the rocket is to make the trip from the Earth to the Moon,a distance of 3.82 * 10⁵ km,in 7.5 hours,what mass of fuel is required? (in kg)

The linear mass density (x)for a one dimensional object is given in the graph shown.What is the location of the center of mass for this object? Express your answer in terms of x₀.

A toy car of mass 4.0 kg is sitting stationary when a child rolls a toy truck of mass 6.5 kg straight towards it in the negative x-direction with a speed of 5.0 m/s.What is the relative momentum?

Two equal masses are connected by an ideal spring and supported in a vertical configuration by only one mass,with the other mass hanging freely.What is the behavior of the bottom mass immediately after the top mass is released?

A uniform wire is bent into a semi-circle of radius R and laid out such that it is entirely in the x-y plane .The semicircle has its ends fixed on the x axis at x = -R and x = +R.With the exception of its end points,the semicircle is entirely above the x-axis (i.e.the y-coordinates of all points on its arc are positive).What is the y coordinate of its center-of-mass?

A flat metal disk has a diameter of 27 cm.A smaller disk with a diameter of 11 cm is then cut out of the larger disk.The hole left behind in the larger disk has its edge located at the center of the larger disk.How far from the center of the larger disk is the center of mass of the larger disk with the circular hole?