91影视

Under what conditions is the momentum of a system constant? Can the $\mathbf{x}$ component of momentum be constant even if the$\mathbf{y}$ component is changing? In what circumstances? Give an example of such behavior.

What is it about analyzing collisions in the center-of-mass frame that simplifies the calculations?

In order to close a door, you throw an object at the door. Which would be more effective in closing the door, a 50g tennis ball or a 50g lump of sticky clay? Explain clearly what physics principles you used to draw your conclusion.

Consider a head-on collision between two objects. Object 1, which has mass ${\mathit{m}}_{\mathbf{1}}$, is initially in motion, and collides head-on with object 2, which has mass${\mathit{m}}_{\mathbf{2}}$and is initially at rest. Which of the following statements about the collision are true?

(1)${\stackrel{\mathbf{鈫�}}{\mathbf{p}}}_{\mathbf{1}\mathbf{\text{,initial}}}\mathbf{=}{\stackrel{\mathbf{鈫�}}{\mathbf{p}}}_{\mathbf{1}\mathbf{,}\mathbf{\text{final}}}\mathbf{+}{\stackrel{\mathbf{鈫�}}{\mathbf{p}}}_{\mathbf{2}\mathbf{,}\mathbf{\text{final}}}$.

(2)$\left|{\stackrel{鈫�}{p}}_{1,\text{final}}\right|\mathbf{<}\left|{\stackrel{鈫�}{p}}_{1\text{, initial}}\right|$.

(3) If${\mathit{m}}_{\mathbf{2}}\mathbf{鈮�}{\mathit{m}}_{\mathbf{1}}$, then$\left|螖{\stackrel{鈫�}{p}}_1\right|\mathbf{>}\left|螖{\stackrel{鈫�}{p}}_2\right|$.

(4) If${\mathit{m}}_{\mathbf{1}}\mathbf{鈮�}{\mathit{m}}_{\mathbf{2}}$, then the final speed of object 2 is less than the initial speed of object 1.

(5) If${\mathit{m}}_{\mathbf{2}}\mathbf{鈮�}{\mathit{m}}_{\mathbf{1}}$, then the final speed of object 1 is greater than the final speed of object 2.

In a nuclear 铿乻sion reactor, each 铿乻sion of a uranium nucleus is accompanied by the emission of one or more high-speed neutrons, which travel through the surrounding material. If one of theneutrons is captured in another uranium nucleus, it can trigger 铿乻sion, which produces more fast neutrons, which could make possible a chain reaction

A ball whose mass is 0.2kg hits the 铿俹or with a speed of 8 m/s and rebounds upward with a speed of 7m/s. The ball was in contact with the 铿俹or for$\mathbf{0}.\mathbf{5}\mathbf{ms}\left(\mathbf{0}.\mathbf{5}脳\mathbf{10}-\mathbf{3}\mathbf{s}\right)$.

(a) What was the average magnitude of the force exerted on the ball by the 铿俹or? (b) Calculate the magnitude of the gravitational force that the Earth exerts on the ball.

(c) In a collision, for a brief time there are forces between the colliding objects that are much greater than external forces. Compare the magnitudes of the forces found in parts (a) and (b).

A projectile of mass${\mathbf{m}}_{\mathbf{1}}$moving with speed ${\mathit{v}}_{\mathbf{1}}$in the +xdirection strikes a stationary target of mass${\mathbf{m}}_{\mathbf{2}}$head-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 if${\mathbf{m}}_{\mathbf{1}}\mathbf{鈮�}{\mathbf{m}}_{\mathbf{2}}$, or if${\mathbf{m}}_{\mathbf{2}}\mathbf{鈮�}{\mathbf{m}}_{\mathbf{1}}$. 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.

Object $\mathbf{A}$ has mass ${\mathbf{m}}_{\mathbf{A}}\mathbf{=}\mathbf{7}\mathbf{}\mathbf{kg}$and initial momentum${\stackrel{\mathbf{鈫�}}{\mathbf{P}}}_{\mathbf{Aj}}\mathbf{=}\mathbf{(}\mathbf{17}\mathbf{,}\mathbf{-}\mathbf{5}\mathbf{,}\mathbf{0}\mathbf{)}\mathbf{kg}\mathbf{.}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$, just before it strikes object B , which has mass ${\mathbf{m}}_{\mathbf{A}}\mathbf{=}\mathbf{11}\mathbf{kg}$. Object B has initial momentum ${\stackrel{\mathbf{鈫�}}{\mathbf{p}}}_{\mathbf{Bj}}\mathbf{=}\mathbf{(}\mathbf{4}\mathbf{,}\mathbf{6}\mathbf{,}\mathbf{0}\mathbf{)}\mathbf{kh}\mathbf{.}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. After the collision, object A is observed to have 铿乶al momentum ${\stackrel{\mathbf{鈫�}}{\mathbf{P}}}_{\mathbf{Af}}\mathbf{=}\mathbf{(}\mathbf{13}\mathbf{,}\mathbf{3}\mathbf{,}\mathbf{0}\mathbf{)}\mathbf{kg}\mathbf{.}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. In the following questions, 鈥渋nitial鈥� refers to values before the collisions, and 鈥滐瑏nal鈥� refers to values after the collision. Consider a system consisting of both objects and . Calculate the following quantities: (a) The total initial momentum of this system. (b) The 铿乶al momentum of object B. (c) The initial kinetic energy of object A. (d) The initial kinetic energy of object B. (e) The 铿乶al kinetic energy of object A. (f) The 铿乶al kinetic energy of object B. (g) The total initial kinetic energy of the system. (h) The total 铿乶al kinetic energy of the system. (i) The increase of internal energy of the two objects. (j) What assumption did you make about Q (energy 铿俹w from surroundings into the system due to a temperature difference)?

Object:$\mathbf{A}$has mass ${\mathbf{m}}_{\mathbf{A}}=\mathbf{7}\mathbf{kg}$and initial momentum${\stackrel{\mathbf{鈫�}}{\mathbf{p}}}_{\mathbf{A},\mathbf{i}}=\left(\mathbf{17},-\mathbf{5},\mathbf{0}\right)\mathbf{kg}路\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$, just before it strikes object $\mathbf{B}$, which has mass ${\mathbf{m}}_{\mathbf{A}}=\mathbf{11}\mathbf{kg}$. Object $\mathbf{B}$has initial momentum${\stackrel{\mathbf{鈫�}}{\mathbf{p}}}_{\mathbf{B},\mathbf{i}}=\left(\mathbf{4},\mathbf{6},\mathbf{0}\right)\mathbf{kg}路\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. After the collision, object $\mathbf{A}$is observed to have 铿乶al momentum ${\stackrel{\mathbf{鈫�}}{\mathbf{p}}}_{\mathbf{A},\mathbf{f}}=\left(\mathbf{13},\mathbf{3},\mathbf{0}\right)\mathbf{kg}路\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. In the following questions, 鈥渋nitial鈥� refers to values before the collisions, and 鈥滐瑏nal鈥� refers to values after the collision. Consider a system consisting of both objects $\mathbf{A}$and$\mathbf{B}$. Calculate the following quantities: (a) The total initial momentum of this system. (b) The 铿乶al momentum of object B. (c) The initial kinetic energy of object A. (d) The initial kinetic energy of object B. (e) The 铿乶al kinetic energy of object A. (f) The 铿乶al kinetic energy of object B. (g) The total initial kinetic energy of the system. (h) The total 铿乶al kinetic energy of the system. (i) The increase of internal energy of the two objects. (j) What assumption did you make about Q (energy 铿俹w from surroundings into the system due to a temperature difference)?

In outer space a rock whose mass is 3kg and whose velocity was$\mathbf{(}\mathbf{3900}\mathbf{,}\mathbf{-}\mathbf{2900}\mathbf{,}\mathbf{3000}\mathbf{)}\mathbf{m}\mathbf{/}\mathbf{s}$struck a rock with mass 13kg and velocity$\mathbf{(}\mathbf{220}\mathbf{,}\mathbf{-}\mathbf{260}\mathbf{,}\mathbf{300}\mathbf{)}\mathbf{m}\mathbf{/}\mathbf{s}$. After the collision, the 3kg rock鈥檚 velocity is$\mathbf{(}\mathbf{3500}\mathbf{,}\mathbf{-}\mathbf{2300}\mathbf{,}\mathbf{3500}\mathbf{)}\mathbf{m}\mathbf{/}\mathbf{s}$. (a) What is the 铿乶al velocity of the 13kg rock? (b) What is the change in the internal energy of the rocks? (c) Which of the following statements about Q (transfer of energy into the system because of a temperature difference between system and surroundings) are correct? (1)$\mathbf{Q}\mathbf{鈮�}\mathbf{0}$ because the duration of the collision was very short. (2)$\mathbf{Q}\mathbf{=}{\mathbf{E}}_{\mathbf{thermal}}$ of the rocks. (3)$\mathbf{Q}\mathbf{鈮�}\mathbf{0}$ because there are no signi铿乧ant objects in the surroundings. (4)$\mathbf{Q}\mathbf{=}\mathbf{鈭�}\mathbf{k}$ of the rocks.