The Physical World I

Spring 2005
MWF 11:30

Instructor: Dr. Bruce Law, CW 327, Tel: 532-1618.


R5. The work required is the same i.e. Work = mgd = 50 x 10 x 2 = 1000J for the first sack and Work = mgd = 25 x 10 x 4 = 1000J for the second sack.

R9. It`s potential energy would double because GPE = mgh where h is the height, hence, if h is twice is large then GPE is twice as large.

R10. The heavier car has twice as much potential energy as the lighter car because GPE = mgh where m is the mass of the car.

R11. GPE = mgh = 1 x 10 x 4 = 40J at an elevation of 4m.

GPE = 80J at an elevation of 8m.

R13. KE = 0.5mv2 = 0.5 x 1 x 2 x 2 = 2J

R14. KE = 0.5mv2 therefore if v increases by a factor of 4 then v2 = 4 x 4 = 16. Namely KE is 16 times larger.

R19. Just before the apple hits the ground the energy is converted to kinetic energy. When the apple hits the ground all of it`s energy is converted to heat and sound energy.



E1. It is easier to stop the lighter truck because it`s KE is less, recall that KE = 0.5m v2 where m is the mass.

E13. The KE is maximum at the bottom of it`s swing where it`s PE is zero. The PE is maximum at the top of it`s swing where it`s KE is zero. When the KE has half of it`s maximum value then the PE will have half of it`s maximum value as well so that the total energy E(tot) = PE + KE remains constant – this is just conservation of total energy.

E26. Both balls will have the same speed according to the conservation of total energy. This is because both tracks have the same height difference between the beginning and the end of the track, therefore, the same amount of gravitational potential energy is converted into kinetic energy.

E28. The golf ball and the Ping-Pong ball both have the same kinetic energy (where KE = mvv/2). As the Ping-Pong ball has the smaller mass m, it must have the higher speed v in order for it to have the same KE as the golf ball. Similarly for light and heavy molecules with the same KE -- the lighter molecule must be moving at a greater speed.

E38. By conservation of energy, the KE is converted into some other form of energy, in this case, heat and sound energy.

E39. The stone should penetrate twice as far because it starts off with twice as much GPE, therefore it will have twice as much KE just before it hits the mud. The mud does work on the stone in order to stop the stone where Work = Fd and F is the friction force acting on the stone. As KE is twice as large the work to stop the stone must be twice as large, therefore assuming the the friction force F stays the same the penetration depth d must be twice as large.



P1. Work = Fd = 10 x 5 = 50J for the first case and Work = Fd = 20 x 2 = 40J for the first case. Assume that all of this work is changed into KE, the first case must produce the large KE.

P2. Friction does work to bring the car to a halt. By conservation of energy therefore, Work = Fd = KE = mvv/2. If the speed v is 3 times greater then the KE is 3x3=9 times greater, hence, the car will skid 9 times as far i.e. 9x15 = 135m.