Exam 8: Systems of Particles and Extended Objects

A circular pizza of radius R has a circular piece of radius R/3 removed from one side,as shown in the figure.The center of mass of the pizza with the hole is at a distance of_____ from the center of mass of the original pizza.

A 25-kg boy jumps off of a 130-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 lake? Ignore the effects of water resistance.

An explosive hockey puck of mass 0.127 kg slides along the ice at 32 m/s in the +x direction,and explodes,sending a 0.037-kg chunk moving in the +x direction at 83 m/s.What is the velocity of the other piece of the puck?

Ignoring air resistance,a catapult on a level field tosses a 5.0-kg stone a horizontal distance of 43 m.A second 5.0-kg stone tossed in an identical fashion breaks apart in the air into 2 pieces,one with a mass of 3.2 kg and one with a mass of 1.8 kg.The breaking apart happens in such a way that both of the pieces hit the ground at the same time.If the 1.8-kg piece lands a distance of 59 m away from the catapult,how far away from the catapult does the 3.2-kg piece land?

A rod has a linear density $\lambda$ = 3x,where x is the distance along the rod,which spans 0 < x < 1 m.What is the coordinate of the center of mass of the rod?

The center of mass of an irregular rigid object is always located

A 4350-kg truck traveling on a bridge at a velocity of (96.2 km/h,45.3 km/h)passes over a 724-kg car traveling at a velocity of (112 km/h,-35.5 km/h).The net momentum of the system consisting of the car and truck is

A carbon monoxide molecule consists of a carbon atom bonded to an oxygen atom.The mass of the carbon atom is 75% the mass of the oxygen atom.The carbon atom is located at the origin and the oxygen atom is located at x = d.Where is the center of mass of the carbon monoxide molecule located?

A thin straight wire of uniform density is oriented in the xy-plane.The ends of the wire are located at (x,y)= (-2.00 m,-1.00 m)and (x,y)= (2.00 m,3.00 m).Where is its center of mass located?

A 25-kg boy jumps off of a raft (m = 92 kg).If the boy jumps off at a speed of 4.40 m/s relative to the lake and the raft moves in the opposite direction with a speed of 1.2 m/s,find the mass of his friend who remains seated on the raft.Ignore the effects of water resistance.

How much force is necessary to keep a 10-cm diameter fire hose stationary if it shoots water at a velocity of 12 m/s?

A long,thin rod lies along the x-axis.One end of the rod is located at x = 2.00 m and the other end of the rod is located at x = 6.00 m.The linear mass density of the rod is given by ,where a = 0.100 kg/ and b = 0.200 kg/m.What is the location of the center of mass of the rod?

Contrary to advice given him,a boy tries bowling on the ice.He releases his 7.3-kg bowling ball when he is sliding at 2.0 m/s,and the ball travels subsequently down the ice at 13 m/s.If,after releasing the ball,the boy is moving backward from his original direction of motion at 0.25 m/s,what is the boy's mass?

A rocket is moving in outer space where no external forces exist.Suppose its mass is m_R and its velocity is v_R at a particular time.When a mass m_F of fuel is ejected,the mass of the rocket becomes (m_R - m_F)and its velocity increases to (v_R+ v_R).Suppose the fuel is always ejected at a constant speed v_F with respect to the rocket.Derive an expression for v_R as a function of m_R given the rocket's initial mass and speed are m₀ and v₀,respectively.

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 magnitude of the position vector of the center of mass of the system is

A long,thin rod lies along the x-axis.One end of the rod is located at x = 2.00 m and the other end of the rod is located at x = 6.00 m.The linear mass density of the rod is given by ,where a = 0.100 kg/ and b = 0.200 kg/m.The mass of the rod is

A large truck of mass 3600 kg approaches a car of mass 1250 kg traveling in the opposite direction.If the velocity of the center of mass of the system is zero,and the truck's speed is 18 m/s,how fast is the car moving?

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 car with respect to the center of mass of the system consisting of the two toys is

Four particles are located at each corner of a square of length 2 cm.If a mass M is located at (x₁,y₁)= (-1 cm,1 cm),a mass 2M is located at (x₂,y₂)= (1 cm,1 cm),a mass 2 M is located at (x₃,y₃)= (1 cm,-1 cm),and a mass M is located at (x₄,y₄)= (-1 cm,-1 cm),where is the center of mass located?

Assume that we have a uniform,square metal plate whose sides measure 6.00 cm and whose mass is 0.325 kg.The plate is located with its lower-left corner at the origin.A 2.00 cm by 2.00 cm square is cut out at the upper-right corner.Find the x-component of the position of the center of mass for the remaining plate.