Question

EXPERIMENT4: THE LINEAR AIR TRACK The aims of this experiment are to: 1)investigate momentum and energy conservation in coll 2. study the cooversion of energy for a body in free fall. There are two types of collisions, elastic and inelastic. In both types of collision momentum is between two bodies in one dimension. The velocity (and hemee the momentum) may be positive or ycorserved. A body of mass m moving with a velocity vi has momentum pi Consider a collision negative. For such a collision the principle of conser-ation of momentum may be written as where p and pe refer to the momenta of the bodies before the collision, and p' and pi refer to the momenta of the bodies after the collision. Iri elastic collisions the kinetic energy is also conserved. The kinetic energy of a body of mass moving with speed v is given by K-% mi. Ifde collision above was elastic then the c of kinetic enmergy is writen as where K, and K refer to the kinetic energies of the bodies before the collision, and Ki' and Ki refer to the kinetic energies of the bodies after the colision. An inelastic collision is defined as a collisioe in which kinetic energy is not coeserved. The total energy of the system is, of course, conserved The gravitational potential energy of a body of mass m at a height h above the surface of the earth is given by where g is the acceleration due to gravity (this is cnly true for h small compared to the earth's radius, Rean-6378 km) In the experiment described later we allow a body of mass m to fall through a height h. This body is connected via a string to a body of mass M that is free to move on a horizontal surface. The two masses accelerate from rest to a final velocity, which is given by the principle of conservation of energy as follows where v is the final velocity of the two masses.

please help with question 4.

Answer 1

See potential energy I.e U=mgh has been derived keeping an assumption that the gravitational field due to earth's surface is constant which starts holding untrue if you move very far away from the center (h becomes in the range of R), in that case the field will become uniform and thus you will have to use integration to then calculate the potential energy.

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