Question

In: Physics

Consider the air tracks from lab: A car of mass m is set in motion with...

Consider the air tracks from lab: A car of mass m is set in motion with constant speed. As it moves down the track a mass of 2m is dropped onto the car without causing any damage. The car and additional load continue along the track. How does kinetic energy of the car + load compare to the original kinetic energy of the car?

1) The kinetic energy is 3 times the original kinetic energy

2) The kinetic energy is equal to the original kinetic energy

3) The kinetic energy is 1/2 times the original kinetic energy

4) The kinetic energy is 1/3 times the original kinetic energy

5) The kinetic energy is 2 times the original kinetic energy

Expert Solution

The momentum of the 2m mass is (2m ) u_o be fore collission with the car

here u_o is initial velocity of the 2m mass.

The momentum of the car before collission is 'mu' here u is the initial velocity of the car.

the total momentum before collission is (2m ) u_o + mu

After the collission 2m mass is along with the car without damage means it is 'inelastic collission'

Therefore the momentum of the system after collission is ( 2m + m ) V here 'V' is the final velocity of the system.

According to law of conservation of energy the total momentum before collission = the total momentum after collission

(2m ) u_o + mu = ( 2m + m ) V

2mu_o + mu = 3m V

2u_o +u = 3V since 'm ' get cancelled on both sides

V = ( 2u_o + u ) / 3 = ( 2u_o /3 ) + ( u / 3 )

since V is 1/3 of the initial velocity of car , u , the final kinetic energy of the system after collission is equal to the 1/3 of the original kinetic energy. [ Note : kinetic energy = ( 1/2 ) m v²

Hence the fourth option of the question is correct.

genius_generous answered 5 months ago

In the Force lab, we use a small lab car with mass m=5 Kg, the experiment...

In the Force lab, we use a small lab car with mass m=5 Kg, the experiment is on a horizontal table, on the car is acting a pulling force F= 20 N and the kinetic friction force Fr is acting as well. The car initially is at rest, and take 6.0 seconds to reach the velocity of 8.5 m/s. a) Calculate the magnitude of the friction force Fr acting on the car? b) We remove the pulling force when the...

A particle with mass m begins its motion from the state of rest under the influence...

A particle with mass m begins its motion from the state of rest under the influence of an oscillating force F(t) = F0 sin(γ t). Find the particle’s velocity and the distance traveled at time t1, when the force reaches its first maximum, and at time t2, when the force becomes equal to zero.

Mass m of your air cart: &nb

Mass m of your air cart: m = 0.185 kg Distance L (=s) from release point to photo gate: L = 1.2 m Angle θ of your air track: θ = 88.5° Mass (kg) Velocity (m/s) Acceleration (m/s2) 0.185 0.79 0.285 0.79 0.385 0.80 Calculate the acceleration Calculate the work done using the change in kinetic energy for each trial. Calculate the work done by the forces on the air cart using W = FL cos (θ) for each...

2) Consider a frictionless horizontal air hockey table. A red disk of mass M and speed...

2) Consider a frictionless horizontal air hockey table. A red disk of mass M and speed 4V travels in the +y direction. It collides elastically with a blue disk at rest. After the collision, the red disk is moving in the -x direction at speed 3V. Find the mass of the blue disk as a function of M.

A problem involves a car of mass m going down a track from a height H,...

A problem involves a car of mass m going down a track from a height H, and round a loop of radius r. The loop is frictionless. It asks for the minimum cut-off speed required, at the highest point in the loop (call it point D), such that the car makes it round the loop without falling. I know the solution; I should set the centripetal accleration equal to 9.81. In other words, contact force with the track at point...

A car of mass M and a small truck of mass 3M are travelling along two...

A car of mass M and a small truck of mass 3M are travelling along two roads perpendicular to each other as shown.The car and the truck collide at the intersection at O. The speed of the truck just before collision is VT =15.0m/s. Immediately after the collision, the wreckage moves as a single mass with Vf =12.0m/s as shown. Using conservation of momentum: [a] Find the value (in degrees) of θ? A car of mass M and a small...

1.a) What is the (average) power needed to accelerate a car of mass m=1550 kg from...

1.a) What is the (average) power needed to accelerate a car of mass m=1550 kg from zero to 60 mph in 7.1 s? b) Which simplifications did you make in that short calculation, i.e. what did you neglect? 2.The current BC hydro rates are 6.55 cents per kWh. If you have a desktop computer that uses 200 W (on average), how much does it cost you per month to run it for 6 hours per day? 3. An elevator car...

Consider a thin uniform disk of mass M and radius R. A mass m is located...

Consider a thin uniform disk of mass M and radius R. A mass m is located along the axis of the disk at a distance z from the center of the disk. The gravitational force on the mass m (in terms of m, M, R, G, and z) is

Consider the following statements: I. The motion of a spring-mass system is a SHO II. The...

Consider the following statements: I. The motion of a spring-mass system is a SHO II. The motion of a pendulum whose amplitude is less than 15 degrees is a SHO Which of the following is true? a. Statement I is true but statement II is false. b. Statement I is false but statement II is true. c. both statements are true. d. Both statements are false. Is an oscillator whose restoring force is F = -kx^2 a simple harmonic oscillator?...

Consider the one-dimensional motion of a particle of mass ? in a space where uniform gravitational...

Consider the one-dimensional motion of a particle of mass ? in a space where uniform gravitational acceleration ? exists. Take the vertical axis ?. Using Heisenberg's equation of motion, find the position-dependent operators ? ? and momentum arithmetic operator ?? in Heisenberg display that depend on time. In addition, calculate ??, ?0, ??, ?0.