BS Math + BS Chemistry (Semester 01) ASSIGNMENT 04 1. Justify the following statement. “The law of conservation of linear momentum, as applied to a single particle, is equivalent to Newton’s first law of motion.” 2. Can the impulse of a force be zero, even if the force is not zero? Explain why or why not. 3. Explain how an airbag in an automobile may help to protect a passenger from serious injury in case of a collision. 4. Why is it that racing drivers actually speed up when traversing a curve? 5. Why do tires grip the road better on level ground than they do when going uphill or downhill? 6. Find the ratio of the linear momenta of two particles of masses 1.0 kg and 4.0 kg if their kinetic energies are equal. 7. Suppose a rubber ball and steel balls collide. Which, if either, receives the larger impulse? Explain. 8. A light object and a heavy object have the same kinetic energy. Which has the greater momentum? Explain. 9. Describe a collision in which all kinetic energy is lost. 1. The bumper of a new car is being tested. The 2300-kg vehicle, moving at 15 m/s, is allowed to collide with a bridge abutment, being brought to rest in a time of 0.54 s. Find the average force that acted on the car during impact. 2. A 75.2-kg man is riding on a 38.6-kg cart traveling at a speed of 2.33 m/s. He jumps off in such a way as to land on the ground with zero horizontal speed. Find the resulting change in the speed of the cart. 3. An object of 2.0-kg mass makes an elastic collision with another object at rest and continues to move in the original direction but with one-fourth of its original speed. What is the mass of the struck object? 4. How fast must an 816-kg Volkswagen travel to have the same momentum as (a) a 2650-kg Cadillac going 16.0 km/h? (b) a 9080-kg truck also going 16.0 km/hr? 5. A pellet gun fires ten 2.14-g pellets per second with a speed of 483 m/s. The pellets are stopped by a rigid wall. (a) Find the momentum of each pellet. (b) Calculate the average force exerted by the stream of pellets on the wall. (c) If each pellet is in contact with the wall for 1.25 ms, what is the average force exerted on the wall by each pellet while in contact? BS Math + BS Chemistry (Semester 01) ASSIGNMENT 05 1. About what axis is the rotational inertia of your body the least? About what axis through your center of mass is your rotational inertia the greatest? 2. If two circular disks of the same weight and thickness are made from metals having different densities, which disk, if either, will have the larger rotational inertia about its symmetry axis? 3. You can distinguish between a raw egg and a hardboiled one by spinning each one on a table. Explain how. Also, if you stop a spinning raw egg with your fingers and release it very quickly, it will resume spinning. Why? 4. Does the center of mass of a solid object necessarily lie within the object? If not, give examples. 5. Can a rocket reach a speed greater than the speed of the exhaust gases that propel it? Explain why or why not. 6. Do the center of mass and the center of gravity coincide for a building? for a lake? Under what conditions does the difference between the center of mass and the center of gravity become significant? Give an example. 7. We claim that momentum and angular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explain. 8. Why is it more difficult to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer this. 9. If the net force on a system is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zero? Explain and give examples. 1. Show that the ratio of the distances x1 and x2 of two particles from their center of mass is the inverse ratio of their masses; that is,x1/x2 = m2/m1 . 2. Calculate the rotational inertia of a meter stick, with mass 0.56 kg, about an axis perpendicular to the stick and located at the 20-cm mark. 3. What is the angular speed of (a) the second hand, (b) the minute hand, and (c) the hour hand of a watch? 4. How far is the center of mass of the Earth–Moon system from the center of the Earth? (From Google, obtain the masses of the Earth and Moon and the distance between the centers of the Earth and Moon. 5. A Plymouth with a mass of 2210 kg is moving along a straight stretch of road at 105 km/h. It is followed by a Ford with mass 2080 kg moving at 43.5 km/h. How fast is the center of mass of the two cars moving?