91影视

Automobiles are designed with 鈥渃rumple zones鈥� intended to collapse in a collision. Use the ideas of this chapter to explain why.

A $2.0kg$object is moving to the right with a speed of $1.0m/s$when it experiences the force shown in FIGURE EX11.8. What are the object鈥檚 speed and direction after the force ends?

A spaceship of mass 2.0 $脳$ 10⁶ kg is cruising at a speed of 5.0 $脳$ 10⁶ m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.0 $脳$ 10⁵ kg, is blown straight backward with a speed of 2.0 $脳$ 10⁶ m/s. A second piece, with mass 8.0 $脳$ 10⁵ kg, continues forward at 1.0 $脳$10⁶ m/s. What are the direction and speed of the third piece?

A 20 kg wood ball hangs from a 2.0-m-long wire. The maximum tension the wire can withstand without breaking is 400 N. A 1.0 kg projectile traveling horizontally hits and embeds itself in the wood ball. What is the greatest speed this projectile can have without causing the wire to break?

A two-stage rocket is traveling at 1200 m/s with respect to the earth when the first stage runs out of fuel. Explosive bolts release the first stage and push it backward with a speed of 35 m/s relative to the second stage. The first stage is three times as massive as the second stage. What is the speed of the second stage after the separation?

The air-track carts in FIGURE CP11.83 are sliding to the right at 1.0 m/s. The spring between them has a spring constant of 120 N/m and is compressed 4.0 cm. The carts slide past a flame that burns through the string holding them together. Afterward, what are the speed and direction of each cart?

Section 11.6 found an equation for v_max of a rocket fired in deep space. What is v_max for a rocket fired vertically from the surface of an airless planet with free-fall acceleration g? Referring to Section 11.6, you can write an equation for 鈭哖_y, the change of momentum in the vertical direction, in terms of dm and dv_y. 鈭哖_y is no longer zero because now gravity delivers an impulse. Rewrite the momentum equation by including the impulse due to gravity during the time dt during which the mass changes by dm. Pay attention to signs! Your equation will have three differentials, but two are related through the fuel burn rate R. Use this relationship鈥攁gain pay attention to signs; m is decreasing鈥攖o write your equation in terms of dm and dv_y. Then integrate to find a modified expression for v_max at the instant all the fuel has been burned.

a. What is v_max for a vertical launch from an airless planet ? Your answer will be in terms of m_R, the empty rocket mass; m_F0, the initial fuel mass; v_ex, the exhaust speed; R, the fuel burn rate; and g.

b. A rocket with a total mass of 330,000 kg when fully loaded burns all 280,000 kg of fuel in 250 s. The engines generate 4.1 MN of thrust. What is this rocket鈥檚 speed at the instant all the fuel has been burned if it is launched in deep space ? If it is launched vertically from the earth?

A golf club continues forward after hitting the golf ball. Is momentum conserved in the collision? Explain, making sure you are careful to identify 鈥渢he system.鈥�

A $2.0kg$object is moving to the right with a speed of $1.0m/s$when it experiences the force shown in FIGURE EX11.9. What are the object鈥檚 speed and direction after the force ends?