Practice Test 2: Newtonian Mechanics (ENG1081 Semester 2- 2015)
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Practice Test 2: Newtonian Mechanics (ENG1081 Semester 2- 2015)
Question A1 (3 + 3 + 2 = 8 marks)
You are given a few objects of unknown mass and you design a few experiments to determine the masses of each of the objects:
(a) Placing a mass on a see-saw 0.5 m to the left of the pivot balances it when a 10 kg mass sits 1m to the right of the pivot. What is this object/s mass?
(b) For the second object of unknown mass, after it collides (perfectly elastically) with a 2 kg mass at rest, the 2 kg mass moves off with a speed of 5 m/s. The initial and final speeds ofthe second object are, respectively, 3.5 m/s and 1.5 m/s. What is this unknown mass?
(c) For the last object you slide it along a frictionless track at 5 m/s and then drop a 10 kg mass straight down onto it. The two masses move together with a speed of 0.5 m/s. What is this unknown mass?
Question A2 (2 + 3 + 3 = 8 marks)
A new planetary system is discovered in which there are two planets in circular orbits. The outer planet orbits with a period that is 8 times that of the inner planet.
(a) What is the ratio of the distances at which the planets orbit, router/rjnner?
(b) If the innermost orbit is at a distance of 1.5 x 108 km, and its period is 1 year, what is the mass of the star (in kg) around which it orbits?
(c) What is the mass of the innermost planet assuming it has a kinetic energy of 2.68 x 1033 J?
Question A3 (2 + 2 + 2 + 3 = 9 marks)
A force of 10 N is applied tangentially to the edge (or rim) of a wheel of diameter 20 cm.
(a) What magnitude torque does this force exert?
(b) Ifthis results in an angular acceleration of the wheel of 0.5 rad/s2, what is the
moment of inertia (i.e., rotational inertia) for the wheel?
(c) What is the mass of the wheel if we treat it as a disc (1 = M R2/2)?
(d) How long does it take for the wheel to reach 30 rpm from rest?
Question A4 (2 + 3 + 3 = 8 marks)
You push a 50 kg crate across the floor, exerting a steady 12 N of horizontal force on the crate. There is a steady frictional force of 10 N opposing your efforts. Only use energy method.
(a) How much work do you do in pushing the crate 5 m?
(b) What is the crate/s speed when you reach the 5 m mark assuming you started from rest?
(c) If you no longer push the crate after reaching the 5 m mark, how much farther will it slide?
Question A5 (7 + 2 + 2 = 7 marks)
Suppose a 2 million kg meteor is initially basically at rest in the asteroid belt, at a distance of 4.0 x 108 km from the Sun. As it falls toward the sun it collides with the Earth (ending up 1.5 x 108 km from the Sun).
(a) What is its kinetic energy just before impact? (Assume throughout that only the gravity of the Sun matters).
(b) The most powerful fission bomb explodes with an energy of 2.1 x 1015 J. The impact energy of the asteroid in (a) is equivalent to how many such bombs? The heaviest asteroid is Ceres which has a mass of 9 x 1020 kg. How many fission bombs is the impact energy of Ceres equivalent to?
(c) What effect does the assumption we made in (a) have on your result in (a)? That is, would the real energy of impact be higher or lower if we do not make this assumption? Explain briefly.
2023-05-29