Year 11 Physics Momentum and Kinetic Energy

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A question asked by students in Year 11 Physics  is "what is the difference between momentum and kinetic energy?" Moving objects have both momentum and kinetic energy but each quantity plays a different role in Physics. A good description of why we need both momentum and kinetic energy is given by Serway and Jewett in Physics for Scientists and Engineers (eighth edition page 236)......There are clear differences between kinetic energy and momentum. First, kinetic energy is a scalar and momentum is a vector. Consider a system of two equal masses heading towards each other on a line with equal speeds. There is kinetic energy associated with this system because members of the system are moving. Because of the vector nature of momentum however, the momentum of this system is zero. A second major difference is  that kinetic energy can transform to other types of energy, such as potential energy or internal energy. There is only one type of linear momentum, so we see no such transformations when using a momentum approach to a problem...

Momentum can be thought of as the tendency of an object to keep moving in a straight line at the same speed. Kinetic energy is  the work done (energy provided) by an external force in moving the object from rest to its final speed.

From a mathematical perspective, in classical physics momentum is defined as mass multiplied by velocity, p=mv and kinetic energy is given by Ek=1/2mv2. Notice that If we differentiate 1/2mv2 with respect to v we get mv which is of course the momentum. This generalisation is one of the first steps in the long road to the development of quantum mechanics. A tutorial sheet on momentum and kinetic energy follows.

  1. Express Ek in terms of p and m.
  2. Two objects P and Q, have masses in the ratio of 2:1 respectively. If each has the same momentum which has the greater kinetic energy?
  3. Two cars are moving along a road. The mass of one car is twice that of the other but it is moving at half the speed of the smaller car. What is the ratio of the kinetic energy of the larger car to that of the smaller car?
  4. Two objects A and B are in motion. The kinetic energy of A is one quarter that of B and the momentum of B is one half that of A. What is the ratio of the speed of A to the speed of B?
  5. A trolley of mass 452g is moving in a straight line on a smooth horizontal laboratory bench. A block of plasticine of mass 146g is initially at rest. Determine the change in kinetic energy of the system when (i) the block is on the bench and the trolley collides with and sticks to the block (ii) the block is dumped on the trolley from a small height as the trolley passes underneath. Describe what has happened in each case to the missing kinetic energy.
  6. A large mass M is at rest on a smooth horizontal table. A smaller mass m moving at a velocity u collides with the larger mass. If the collision is perfectly elastic determine the velocity of the smaller mass after the collision.
  7. In the previous question initially the larger mass M is moving at a velocity U and the smaller mass m is at rest. Determine the velocity of m after the collision.
  8. A trolley of mass M contains a mass m of sand. The loaded trolley moves at a velocity U along a smooth horizontal laboratory bench. The sand starts to leak from the trolley at a constant rate R. Determine the velocity of the trolley when one half of the sand has leaked out.
  9. *Three perfectly elastic spheres of masses m1,m2 and m3 lie in that order and not in contact in a smooth horizontal groove. If m1 is projected towards m2 with velocity U find the velocities of each sphere after two impacts have occurred and show that there will not be a third if m2(m1+m2+m3)>3m1m3

 

 

 

HSC Physics Space

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With the old Space topic being examined for the last time this November a list of true-false questions on concepts that are often misunderstood is given below. This list will be updated during the year.

Gravity

  1. A satellite has a greater gravitational potential energy than a grain of dust in the same circular orbit about the Earth.
  2. Gravitational potential energy is the energy needed to bring masses together from a state where they are not influencing each other.
  3. A gravitational sling-shot of a spacecraft by Jupiter causes the spacecraft to leave Jupiter at a greater speed. [false, spacecraft can increase speed relative to the Sun by "taking" kinetic energy from Jupiter in an interaction in which the spacecraft has no change in kinetic energy in Jupiter's reference frame but an increase in KE in the Sun's reference frame due to Jupiter slowing down and giving KE to the spacecraft. The final spacecraft speed can be increased by almost twice the speed of Jupiter if the spacecraft moves directly towards the approaching planet whose gravitational field sweeps it around increasing its speed relative to the Sun]
  4. Two large equal masses M are placed a distance r apart. A smaller mass m is placed at the midpoint of the line joining the larger masses. The gravitational potential energy of this system is zero.
  5. Two large masses M are placed a distance r apart. The work done in moving a mass m from a very large distance to the midpoint of the line joining the larger masses depends on the path taken.
  6. Gravitational potential energy increases as a mass moves closer to the Earth since the gravitational force increases.
  7. A mass is tied to a string of length 120 cm and moves freely in a vertical circle in the Earth's gravitational field. The speed of the mass at its lowest point is 8.0 ms -1 . The magnitude of the acceleration of the mass at this instant is 53.3 ms -2 .[false,54.2 ms -2 ]


Projectiles

  1. A projectile moving upwards has a negative acceleration and when it moves downwards its acceleration is positive.
  2. A cannon is fired horizontally from a tall mountain. The projectile can strike the Earth on the hemisphere opposite to the direction of firing if its initial speed is sufficient.
  3. An object is dropped from the Eiffel Tower. Neglecting air resistance the object hits the ground at a point to the east and south of its starting point. An object dropped from Centre Point Tower (neglecting air resistance) will be deflected to the west and north of its starting point.
  4. A ball is thrown at initial speed U on horizontal ground. The maximum range of the ball is R. If the new initial speed is 2U the maximum range (neglecting air resistance) is 2R.

Orbits

  1. The two forces acting on a satellite moving in a circular path around a planet at a constant speed with no air drag are the gravitational force and the centripetal force.
  2. When atmospheric drag acts on a satellite its speed decreases.
  3. Apollo 13 could re-enter the Earth's atmosphere at an angle 𝜽 to the vertical where 5.3° < 𝜽 < 7.7°.
  4. A spacecraft that bounces off the atmosphere enters an orbit around the Sun.
  5. A satellite is in a low Earth circular orbit. The radius of the orbit decreases. The gain in orbital kinetic energy of the satellite is equal to the loss in gravitational potential energy of the satellite.
  6. A satellite in a high Earth circular orbit has a total energy E. If the satellite is placed in a circular orbit of twice the radius its total energy is 2E.
  7. A satellite in a circular orbit of period 23h 56m 4s that passes over Sydney always appears directly overhead.

Relativity

  1. An electron cannot move through water at a speed greater than the speed of light in water.
  2. A rocket moves at a constant velocity of 0.90c relative to the Earth. The crew of the rocket play a CD that lasts for 1 hour. A person on the Earth plays an identical CD that lasts for a longer time interval than one hour.
  3. A particle accelerator is 2.0 km long. A proton starts from rest and moves through the accelerator striking the end at 0.8c. The distance travelled by the proton in its own reference frame is 1.2km.
  4. A certain star is 66.5 light-years away from the Earth. A spacecraft leaves the Earth and travels at a constant speed of 0.95c to the star. The time taken to travel to the star according to a clock on the spacecraft is 70 years.
  5. A train is moving to the east. A ball is rolled across the smooth floor of the train initially perpendicular to the south side of the train at 1 ms -1 .A person in the train sees the ball move in a parabolic arc towards the east of focal length 1 m. The acceleration of the train is 0.5 ms -2 to the east.
  6. A white hot metal rod is cooled to room temperature.Its mass does not change.
  7. In Michelson and Morley's interferometer the light rays interfere destructively. This is called a null result.
  8. In the aether theory the time taken by light to travel along each of the equal arms of the interferometer is the same.
  9. Interference fringes are not caused by the reflections from the half silvered mirror in the Michelson-Morley experiment.

  10. The result of the Michelson-Morley experiment is that the time taken by light to travel a given path depends on the direction of the light ray.

  11. Simultaneous events are seen to happen at the same time instant in the same reference frame.

  12. Michelson and Morley measured a change in fringe spacing when they rotated their apparatus through 90°
  13. Michelson and Morley expected to measure a change in fringe spacing when they rotated their apparatus through 90°