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Chapter 10: Q1 (page 410)

Under what conditions is the momentum of a system constant? Can the x component of momentum be constant even if they component is changing? In what circumstances? Give an example of such behavior.

Short Answer

Expert verified

The momentum of a system is constant if there is no net vector force on the system.

Yes, the xcomponent of momentum be constant even if the ycomponent is changing if the object is moving in xz plane.

Step by step solution

01

Significance of the momentum of a system

Momentum is defined as the product of the mass and velocity of the object and it can be changed by applying the force to the object. So, it can be constant if no external force acts on the system.

02

Identification of the condition of the constant momentum of a system

In the case when net vector forces are not acting on the system, then the momentum is said to be constant.

Assume that a ball is moving in xzplane. In this condition, gravitational force and centripetal force will act in ydirection only that will result in the change in the ycomponent of the momentum. There will not be any force that will act in xdirection , so there is no change in the xcomponent of the momentum.

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Most popular questions from this chapter

Consider a head-on collision between two objects. Object 1, which has mass m1, is initially in motion, and collides head-on with object 2, which has massm2and is initially at rest. Which of the following statements about the collision are true?

(1)p→1,initial=p→1,final+p→2,final.

(2)|p→1,final|<|p→1, initial|.

(3) Ifm2≫m1, then|Δp→1|>|Δp→2|.

(4) Ifm1≫m2, then the final speed of object 2 is less than the initial speed of object 1.

(5) Ifm2≫m1, then the final speed of object 1 is greater than the final speed of object 2.

It has been proposed to propel spacecraft through the Solar System with a large sail that is struck by photons from the Sun.

(a). Which would be more effective, a black sail that absorbs photons or a shiny sail that reflects photons back toward the Sun? Explain briefly

(b). Suppose thatphotons hit a shiny sail per second, perpendicular to the sail. Each photon has energy. What is the force on the sail? Explain briefly

In outer space, rock 1 whose mass is5Kg and whose velocity was(3300,-3100,3400)m/s struck rock 2, which was at rest. After the collision, rock 1’s velocity is(2800,-2400,3700)m/s . (a) What is the final momentum of rock 2? (b) Before the collision, what was the kinetic energy of rock 1? (c) Before the collision, what was the kinetic energy of rock 2? (d) After the collision, what is the kinetic energy of rock 1? (e) Suppose that the collision was elastic (that is, there was no change in kinetic energy and therefore no change in thermal or other internal energy of the rocks). In that case, after the collision, what is the kinetic energy of rock 2? (f) On the other hand, suppose that in the collision some of the kinetic energy is converted into thermal energy of the two rocks, where∆Ethermal,1+∆Ethermal,2=7.16×106J . What is the final kinetic energy of rock 2? (g) In this case (some of the kinetic energy being converted to thermal energy), what was the transfer of energy Q (microscopic work) from the surroundings into the two-rock system during the collision? (Remember that Q represents energy transfer due to a temperature difference between a system and its surroundings.)

A projectile of massm1moving with speed v1in the +xdirection strikes a stationary target of massm2head-on. The collision is elastic. Use the Momentum Principle and the Energy Principle to determine the final velocities of the projectile and target, making no approximations concerning the masses. After obtaining your results, see what your equations would predict ifm1≫m2, or ifm2≫m1. Verify that these predictions are in agreement with the analysis in this chapter of the Ping-Pong ball hitting the bowling ball, and of the bowling ball hitting the Ping-Pong ball.

A charged pion ( mpc2= 139.6 MeV) at rest decays into a muon (mμ= 105.7 MeV) and a neutrino (whose mass is very nearly zero). Find the kinetic energy of the muon and the kinetic energy of the neutrino, in MeV (1 MeV = 1×106eV).
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