A 0.150-kg frame, when suspended from a coil spring, stretches the spring 0.0400 m. A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm. Find the maximum distance the frame moves downward from its initial equilibrium position.

The equation $F=-v_{e x}(d m / d t)$ for the thrust on a rocket, can also be applied to an airplane propeller. In fact, there are tuo contributions to the thrust: one positive and one negative. The positive contribution comes from air pushed backward, away from the propeller (so $d m / d t<0$ ), at a speed $v_{\mathrm{ex}}$ relative to the propeller. The negative contribution comes from this same quantity of air flowing into the front of the propeller (so $d \mathrm{~m} / \mathrm{dt}>0$ ) at speed $v$, equal to the speed of the airplane through the air. a) Write an equation for the net thrust developed by an aircraft propeller in terms of $U, U_{e x}$, and the absolute value $|d m / d t|$. b) For a Cessna 182 (a single-engine airpllane) flying at $130 \mathrm{~km} / \mathrm{h}, 150 \mathrm{~kg}$ of air flows through the propeller each second and the propeller develops a net thrust of $1300 \mathrm{~N}$. Determine the speed increase (in $\mathrm{km} / \mathrm{h}$ ) that the propeller imparts to the air.

Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide with a glancing blow. Asteroid $A$, which was initially traveling at $40.0 \mathrm{~m} / \mathrm{s}$, is deflected $30.0^{\circ}$ from its original direction, while asteroid $B$, which was initially at rest, travels at $45.0^{\circ}$ to the original direction of $A$. Find the speed of each asteroid after the collision.

A 1500-kg sedan goes through a wide intersection traveling from north to south when it is hit by a 2200-kg SUV traveling from east to west. The two cars become enmeshed due to the impact and slide as one thereafter. On-the-scene measurements show that the coefficient of kinetic friction between the tires of these cars and the pavement is 0.75, and the cars slide to a halt at a point 5.39 m west and 6.43 m south of the impact point. How fast was each car traveling just before the collision?

A belt of asteroids is located an average distance of 503 million kilometers from the sur. Between which two planets is this belt located?

(1) Mars and Jupiter

(2) Mars and Earth

(3) Jupiter and Saturn

(4) Saturn and Uranus

Starling at t=0 a net external force in the +x-direction is applied to an object that has mass 2.00 kg. A graph of the force as a function of time is a straight line that passes through the origin and has slope 3.00 N/s. If the object is at rest at t=0, what is the magnitude of the force when the object has reached a speed of 9.00 m/s?

A small wooden block with a mass $0.800 \textrm{ kg}$ is suspended from the lower end of a light cord that is $1.60 \textrm{ m}$ long. The block is initially at rest. A bullet with a mass $12.0 \textrm{ g}$ is fired at the block with a horizontal velocity $v_{0}$. The bullet strikes the block and becomes embedded in it. After the collision the combined object swings on the end of the cord. When the block has risen to a vertical height of $0.800 \textrm{ m}$, the tension in the cord is $4.80 \textrm{ N}$. What was the initial speed $v_{0}$ of the bullet?

A railroad handcar is moving along straight, frictionless tracks with negligible air resistance. In the following cases, the car initially has a total mass (car and contents) of 200 kg and is traveling east with a velocity of magnitude 5.00 m/s. Find the final velocity of the car in each case, assuming that the handcar does not leave the tracks. (a) A 25.0-kg mass is thrown sideways out of the car with a velocity of magnitude relative to the car’s initial velocity. (b) A 25.0-kg mass is thrown backward out of the car with a velocity of relative to the initial motion of the car. (c) A 25.0-kg mass is thrown into the car with a velocity of relative to the ground and opposite in direction to the initial velocity of the car.

A railroad handcar is moving along straight, frictionless tracks with negligible air resistance. In the following cases, the car initially has a total mass (car and contents) of $200 \mathrm{~kg}$ and is traveling east with a velocity of magnitude $5.00$ m$/$s. Find the $\it{final}$ $\it{velocity}$ of the car in each case, assuming that the handcar does not leave the tracks.
($c$) A $25.0$-$\mathrm{kg}$ mass is thrown into the car with a velocity of $6.00$ m$/$s relative to the ground and opposite in direction to the initial velocity of the car.

In a game of physics and skill, a rigid block (A) with mass m sits at rest at the edge of a frictionless air table, 1.20 m above the floor. You slide an identical block (B) with initial speed $v_{B}$ toward A. The blocks have a head-on elastic collision, and block A leaves the table with a horizontal velocity. The goal of the game is to have block A land on a target on the floor. The target is a horizontal distance of 2.00 m from the edge of the table. What is the initial speed $v_{B}$ that accomplishes this? Neglect air resistance.

Friends Burt and Ernie stand at opposite ends of a uniform log that is floating in a lake. The log is 3.0 m long and has mass 20.0 kg. Burt has mass 30.0 kg; Ernie has mass 40.0 kg. Initially, the log and the two friends are at rest relative to the shore. Burt then offers Ernie a cookie, and Ernie walks to Burt’s end of the log to get it. Relative to the shore, what distance has the log moved by the time Ernie reaches Burt? Ignore any horizontal force that the water exerts on the log, and assume that neither friend falls off the log.

Show that the sequence is bounded. $a_{n}=\frac{6 n-1}{n+3}$

A railroad handcar is moving along straight, frictionless tracks with negligible air resistance. In the following cases, the car initially has a total mass (car and contents) of $200 \mathrm{~kg}$ and is traveling east with a velocity of magnitude $5.00$ m$/$s. Find the $\it{final}$ $\it{velocity}$ of the car in each case, assuming that the handcar does not leave the tracks. (a) A $25.0$-$\mathrm{kg}$ mass is thrown sideways out of the car with a velocity of magnitude $2.00$ m$/$s relative to the car's initial velocity.

The Harris family is planning to buy a new 46-inch HDTV that costs $488. Mr. and Mrs. Harris will pay$200 and their three sons will split the remaining cost equally. Explain how to find the amount each of the boys will pay.