Transcript Day 3
Day 3 HW Problem 2-83 • Hot summer day. Swimmers jump from a bridge into the river below. They hit the water 1.5 s after they stepped off the bridge. ? How high was the bridge ? ? How fast were the swimmers moving when the hit the water ? ? What would be swimmers’ drop time be if the bridge were twice as high ? HW Problem 2-87 • Standing at the edge of a cliff 32.5 m high, you drop a ball. Later, you throw a second ball downward with an initial speed of 11.0 m/s. • (a) which ball has the greater increase in speed when it reaches the base of the cliff, or do both balls speed up by the same amount? • (b) do the calculations. HW Problem 2-90 • A hot-air balloon is descending at a rate of 2.0 m/s when a passenger drops a camera. If the camera is 45 m above the ground when it is dropped, • (a) how long does it take for the camera to reach the ground? • (b) what is its velocity just before it lands? HW Problem 2-102 • • • • Drop Tower 2.2 second of free fall ? What is the drop distance of a 2.2-s tower? ? How fast are the experiments traveling when they hit the air bags at the bottom of the tower? ? If the experimental package comes to rest over a distance of 0.75 m upon hitting the air bags, what is the average stopping acceleration? HW Problem 3-10 • A lighthouse that rises 49 ft above the surface of the water sits on a rocky cliff that extends 19 ft from its base. A sailor on the deck of a ship sights the top of the lighthouse at an angle of 30.0o above the horizontal. If the sailor’s eye level is 14 ft above the water, how far is the ship from the rocks? HW Problem 3-24 • Vector A points in the negative x direction and has a magnitude of 22 units. The vector B points in the positive y direction. • (a) Find the magnitude of vector B if the sum of vector A and vector B has a magnitude of 37 units. HW Problem 3-32 Unit vectors Find the direction and the magnitude of (a) Vector A = 25 m x direction, -12 m y direction (b) Vector B = 2.0 m x direction, 15 m y direction (c) Vector A + Vector B HW 3-44 A skateboarder rolls from rest down an inclined ramp that is 15.0 m long and inclines above the horizontal at an angle of q = 20.0o. When she reaches the bottom of the ramp 3.00 s later her speed is 10.0 m/s. Show that the average acceleration of the skateboarder is g sin q, where g = 9.81 m/s2. HW Problem 3-51 As you hurry to catch your flight at the local airport, you encounter a moving walkway that is 85 m long and has a speed of 2.2 m/s relative to the ground. If it takes you 68 s to cover 85 m when walking on the ground, how long will it take you to cover the same distance on the walkway? Assume that you walk with the same speed on the walkway as you do on the ground. HW Problem 3-82 • If the dragonfly approaches its prey with a speed of 0.950 m/s, what angle q is required to maintain a constant line of sight parallel to the x axis? • Assume the prey moves with a constant speed of 0.750 m/s. HW Problem 4-15 Playing shortstop, you pick up a ground ball and throw it to second base. The ball is thrown horizontally, with a speed of 22 m/s, directly toward point A. When the ball reached the second baseman 0.45 s later, it is caught at point B. (a) How far were you from the second baseman? (b) What is the distance of vertical drop, AB? HW Problem 4-19 In Denver, pumpkins are dropped from a tower. Suppose the tower is 9.0 m high and that the bull’s-eye is a horizontal distance of 3.5 m from the launch point. If the pumpkin is thrown horizontally, what is the launch speed needed to hit the bull’s-eye? Section 4-4, General Launch Angle y = yo + voyt - ½ ay t2 yo = altitude at the start voyt = how much altitude gained at time t, “up” ½ ay t2 = how much altitude lost at time t, “down” ay usually = g Example 4-5, “A Rough Shot” Lovely picture of a clean parabola, a golf ball as the “projectile,” illustrating one reason to use a golf club with a large angle, for loft, for getting over a tree. Howitzers and mortars are used for the same reason, to shoot over an obstacle. Place Kicker • • • • • Kick from surface Distance to goal posts = 36.0 m Height of crossbar = 3.05 m Angle of kick above horizontal, q, =53o Speed of kick = 20.0 m • ? Does the kick clear the crossbar ? Tiger Woods • Shot hit at q of 26o • Speed of ball off tee = 40.0 m/s? • ? What are the components of his shot, voy and vox ? • ? What is the max height of the flight of the ball ? • ? What is the range of the shot ? Max Height of Projectile • • • • Projectile of mass m Launched at angle q with horizontal Takes time t to get to max altitude h If no gravity, it would reach altitude H Use equations 2.12 and 2.9 to show that h=H/2 Laws of Motion • Newton #1: Object moves with a velocity that is constant in magnitude and direction unless acted on by a non-zero net force. • Newton #2: The acceleration of an object is proportional to the net force acting on the object and inversely proportional to the object’s mass. • Unit of force is kg m / s2 = Newton “N” Lab #2 • An object with a mass of 5.00 kg rests on a frictionless horizontal table. It is connected to a cable that passes over a pulley and is then fastened to a 10.0-kg hanging object. • Find the acceleration of each object and the tension in the cable. Bullet in Rifle • A 5.0-g bullet leaves the muzzle of a rifle with a speed of 320 m/s. • ? What force (assumed constant) is exerted on the bullet while it is traveling down the 0.82m-long barrel of the rifle ? Force during bounce After falling from rest from a height of 30 m, a 0.50-kg ball rebounds upward, reaching a height of 20 m. ? If the contact between ball and ground lasted 2.0 ms, what average force was exerted on the ball ? Free body diagrams Sketch the object in its environment Choose convenient coordinate system Sketch all the forces Resolve the forces into components Apply Newton’s Laws along each coordinate Forces add as Vectors • N#2: total force = mass * acceleration • Acceleration = sum of all forces / mass Newton’s Third Law of Motion N#3: For every force that acts on an object, there is a reaction force acting on a different object that is equal in magnitude and opposite in direction. You proved that this is true in Wednesday’s lab, #3. Pulling the car from the ditch • Two forces are applied to a car in an effort to move it. (a) what is the resultant of these two forces? • (b) If the car has a mass of 3000 kg, what acceleration does it have? • Ignore friction. Runaway (sliding) car Car of mass m Slope of driveway q ? What is the acceleration of the car ? Length of driveway, l, is 25.0 m ? What is time to slide to the bottom ? ? What is the velocity at the bottom ? Lab for Newton’s #3 • Who wins tug of war? • If fk(1) is greater than fk(2), rope will move toward (1) • Big guys in (1) • Shoes with cleats in (1) • Assume: Hands strong enough that the rope doesn’t slip.