2-1 A gardener, who has a roof garden on the top of a tall building, accidentally drops a flower pot, which falls to the sidewalk below. Mercifully, no one is hurt. An observer on a neighboring building  who happens to catch the whole thing on videotape, measures the velocity of the flower pot at two different times and then calculates what it should be in the absence of air friction.

Given: The observer measures the velocity of the flower pot after it has fallen for a time t₁ = 3.0 s and t₂ = 4.0 s

Find: (a) What should be the velocity of the flower pot at t₁ in the absence of air friction? [29.4 m/s]

(b) What should be the velocity of the flower pot at t₂? [39.2 m/s]

(c) How far should the flower pot travel, in free fall, between t₁ and t₂? [34.3 m]

2-B21 A speeding car passes a highway patrol checkpoint and then decelerates at a constant rate.

Given: At a time of 5.0 s after passing the checkpoint, the car is 176 m from the checkpoint and its speed is 25 m/s.

Find (a) What was the car's velocity when it passed the check point? [45 m/s]

(b) What was the acceleration of the car? [-4.1 m/s]

3-1 A rifle bullet is accelerated at a relatively constant rate by burning gunpowder to emerge from the muzzle at near the speed of sound. Meanwhile, the same force acts on the rifle to accelerate it in the opposite direction.

Given: The bullet has a mass of 25 g and emerges from the muzzle at 344 m/s after having accelerated over a distance of 80 cm. The rifle has a mass of 1.8 kg.

Find (a) What is the acceleration of the bullet? [7.40E4 m/s]

(b) How great is the force acting on the bullet? [1.85 kN]

(c) What is the acceleration of the rifle? [1.03E3 m/s]

3-C4(revised) An open paint bucket is attached to another bucket by a light rope that goes up and over a small frictionless pulley. The heavy bucket rests on a window sill while the light bucket rests on the ground. Needless to say, an accident happens and the heavy bucket slips off the window sill.

Given: The heavy bucket has a mass of 12 kg while the light bucket has a mass of 9 kg. The rope is 21 m long and the window sill is 9 m above the ground.

Find: (a) If there is no slack in the rope, what is the acceleration of the big bucket, once it slips off the window sill? [1.4 m/s]

(b) After what time will the first big splash occur? [2.5 s]

4-1 (Based on 4-B12) In San Francisco's Exploratorium, a beautiful mechanics exhibit, called the Giant Pendulum, features a huge concrete and steel pendulum bob attached by a strong cable to the ceiling. Visitors can accelerate this huge object with small forces applied by refrigerator magnets attached to strings. After little experimentation, you learn how hard you can pull on the string before the magnet comes loose from the bob. Another thing you can do is a static force experiment.

Given: The bob is supported by a cable 30 m long and is pulled 15 cm to the side by a horizontal string attached to a 250g pocket knife. The string then goes upward and outward to your hand at an angle of 45^o measured to the horizontal.

Find (a) How much tension is in the part of the string going to your hand? [3.46 N]

(b) How tension is in the horizontal part of the string going to the Giant Pendulum bob? [2.5 N]

4-2. A picture frame is supported by a wire having breaking tension called the "test strength" of the wire, of somewhat more than half the weight of the picture..

Given:  The test strength of the wire is 340 N, and the picture, together with the frame, weights 430 N. the support points on the frame to which the wire is attached are 85 cm apart.

Find (a) What is the minimum angle the wire can make with the horizontal before it breaks? [39.2 degrees]

(b) What is the minimum length of wire necessary to support the picture frame? [1.10 m]