Download Physics 30 2.5 - Free Falling Bodies

Physics 30 2.5 ­ Free Falling Bodies
Physics 30
Unit 2 ­ Mechanics and Force
Lesson 2.5 Outline
You will learn:
• Free Fall and Forces
• how air resistance • Air Resistance
affects the velocity of • Terminal Velocity
a falling object
• Examples
• how to solve problems involving free fall and force
Free Fall
What happens when we drop an object? It starts at rest, but does it fall at a constant rate?
Free fall is the state of an object when the only force acting on an object is gravity, or its weight. We will neglect air resistance to simplify this section.
During freefall, an object will accelerate at a rate that depends on the gravitational field present.
Physics 30 2.5 ­ Free Falling Bodies
One thing to note is that this acceleration is the same for any mass. That is, all objects fall at the same rate in a vacuum even though the forces experienced are different.
When an object is in ‘free fall’ air resistance is present in situations we encounter outside the classroom. Air resistance is a force that gradually grows as an object gains speed.
This is the equal to the weight of the object at terminal velocity.
If air resistance is constantly growing, but the force of gravity remains constant, then during an object’s fall the two forces will eventually equal each other. At this point, the net force on the object will be 0 N.
As the time increases, air resistance increases.
Physics 30 2.5 ­ Free Falling Bodies
When the net force is equal to 0 N, Newton’s law says the mass cannot accelerate. Thus, at this point the object is falling at its maximum velocity. This velocity is called the terminal velocity.
Most people in a regular skydive (belly to the ground) can reach a terminal velocity of around 125 mph. If the orientation is changed to head‐down, the terminal velocity increases to about 150 ‐ 200 mph. Why is this the case?
??
Joseph (Henry) Kittinger actually was able to achieve a velocity of 988 km/h in 1960 by using a balloon to go 31 km above the surface of the Earth. He worked for the US Army Link 1
during this time. More recently, a man named Felix Baumgartner jumped from 39 km as part of a project by Red Bull and actually broke the sound barrier (he achieved 1347 km/h, the speed of sound is about 1225 km/h) during a skydive. Link 2
Physics 30 2.5 ­ Free Falling Bodies
Ex) An 2.0 kg object is dropped from a height of 80.0 m. Determine:
a) the velocity at 2.00 s.
Ex) An 2.0 kg object is dropped from a height of 80.0 m. Determine:
b) the distance travelled in 2.00 s.
Physics 30 2.5 ­ Free Falling Bodies
Ex) An 2.0 kg object is dropped from a height of 80.0 m. Determine:
c) the force pulling it towards the ground
Ex) An 3.5 kg object is shot upward at 49.1 m/s. Determine:
a) the time it takes to reach the maximum height.
Physics 30 2.5 ­ Free Falling Bodies
Ex) An 3.5 kg object is shot upward at 49.1 m/s. Determine:
b) the maximum height it reaches.
Ex) An 3.5 kg object is shot upward at 49.1 m/s. Determine:
c) the force pulling it downwards.
d) The object is accelerated in the barrel of a cannon for 0.125 seconds. What is the force applied while it is in the cannon?
Physics 30 2.5 ­ Free Falling Bodies
2.5 ‐ Free Fall Problems
1.
Taking into account air resistance, sketch the actual shape of the velocity‐time graph for a volleyball dropped from the top of the Calgary tower.
2.
A penny is dropped from the top of a 176.4 m high building. Calculate:
a) the speed at 3.00 s.
b) the distance it falls in the fourth second.
c) the time it take to fall to the ground.
3.
George starts his stopwatch just as he drops it from the top of a building. When he recovers it on the pavement it is smashed and reads 5.10 seconds.
a) How high was the building?
b) With what speed did the watch hit the pavement?
c) How long did it take the watch to fall the first 44.1 m?
4.
A penny is dropped from the top of a 122.5 m high building. Calculate:
a) the velocity after 2.00 s.
b) the distance it will fall in the third second.
c) how long it will take to reach the ground.
5.
A student drops his physics text from the top of a 78.4 m tall building. a) What is the velocity of the text after 2.00 s?
b) How long it will take to reach the ground?
c) How far above the ground is the text after 3.00 seconds?
6.
A golf ball is dropped from a ledge 30.6 m high. Calculate:
a) the distance it falls in one second.
b) the velocity it has at the end of two seconds.
c) the time for the golf ball to fall the 30.6 m.
7.
A penny is dropped from a bridge into the river below.
a) How fast will it be moving 1.50 s after it is dropped?
b) How far will the penny fall in the first two seconds?
c) If the bridge is 44.1 m high, how long will it take the penny to hit the water?
8.
A 5.00 kg shot is dropped from a height of 2.00 m. How much force would be required to stop the shot put in a distance of 50.0 cm?
9.
A man throws a ball straight down at a velocity of 10.0 m/s from a helicopter hovering at an altitude of 590 m. a) What is the velocity of the ball after 5.00 s?
b) What is the acceleration of the ball after 6.00 seconds?
c) How far above the ground is the ball after 10.0 seconds?
d) How far does the ball fall in the third second?
10. A ball is thrown straight down with an initial velocity of 4.90 m/s from the top of a building that is 122.5 m high.
a) What is its velocity after 3.00 s?
b) How far does it fall in the first second?
c) If it had been released from rest, how long would it take to fall to the ground?
11. A man at the top of a building throws a ball downward with an initial velocity of 40.0 m/s. Find the forward displacement of the ball at the end of two seconds, and the displacement if the initial velocity had been 0 m/s.
12. A baseball is thrown vertically upward at 24.5 m/s. Calculate:
a) how long it will be in the air.
b) the maximum height it will reach.
c) when it will have a speed of 9.80 m/s.
13. An arrow is shot by an archer upward at a velocity of 58.8 m/s.
a) To what maximum height does the arrow rise?
b) How long does it take the arrow to get back to the ground?
c) What it the velocity of the arrow after 8.00 s?
d) What is the acceleration of the arrow after 6.00 s ?
e) How high above the ground is the arrow after 2.00 s?
f) How much does the arrow rise in the third second?
14. A small cannonball is fired vertically upward at 196 m/s.
a) If it has a mass of 1.50 kg what does it weigh?
b) What is the acceleration of the cannonball at its maximum height?
c) What is the maximum height it will reach?
d) How long is the cannonball in the air?
15. A small rocket is fired vertically upward at 68.6 m/s.
a) How fast will it be going after 10.0 s?
b) How far above the ground will it be at that time?
c) How far will it rise?
d) How long will it remain in the air?
16. A ball of mass 0.125 kg is thrown upward with an initial velocity of 20.0 m/s.
a) How fast will the ball be moving after 1.00 s?
b) How fast will it be moving 3.20 s after it was thrown?
c) How high does the ball rise above the thrower’s hand?
d) When is its velocity the greatest?
e) When is its acceleration the greatest?
17. A ball is thrown upward at 49.0 m/s.
a) What is the acceleration?
b) How fast will it be moving 2.00 s after it was thrown?
c) How high does the ball rise above the thrower’s hand?
Physics 30 2.5 ­ Free Falling Bodies
Two Body Problems
18. A rock is dropped from the top of a building 245.0 m tall. A ball is shot upward at the same time. How fast was the ball fired if they meet at the half way point?
19. Pete is standing on the roof of a building that is 122.5 m high. Joe is at an open window 14.0 m below the roof. One second after Pete drops a stone, Joe is going to throw a ball straight down from the window. How fast must Joe throw the ball if it is to hit the ground at the same instant the stone does?
20. A block is thrown down at an initial velocity of 9.80 m/s from the top of a cliff 58.8 m high. At the same instant an arrow is shot straight upward at the block of wood with an initial velocity of 19.6 m/s. How long will it take for the block of wood and arrow to meet?
21. A stone is thrown down from the top of a cliff at an initial velocity of 10 m/s at the same instant that a ball is thrown up from the base of the cliff at an initial velocity of 20 m/s. If the cliff is 45.0 m high:
a) how long will it take the ball and stone to meet?
b) what is the velocity of the ball when they meet?
22. A quarter is dropped from the top of a cliff 100 m high. At the same instant a penny is thrown up from the base of the cliff. How fast must the penny be thrown if it is to meet the quarter when the penny is at its highest point?
23. A stone is thrown straight down form the top of a cliff at a speed of 4.90 m/s, at the same instant that a ball is thrown vertically up from the base of the cliff at a speed of 39.2 m/s. If the cliff is 87.2 m high, how far apart will the stone and ball be when the downward speed of the stone is the same as the upward speed of the ball?
24. A stone is dropped from the top of a building. One second later a ball is thrown down after it at an initial velocity of 24.5 m/s. Which object is ahead and by how much at the point in time when the ball is moving twice as fast as the stone?
25. Bill and Bob are both on the roof of a building that is 176.4 m high. Bill drops a penny straight down at the same instant that Bob throws a dime vertically upwards. The dime is thrown over the edge such that when it comes back down it misses the roof and follows the penny to the street below. How fast was the dime thrown if when the penny hits the ground the dime is still at a height of 58.8 m?
26. The two masses in the diagram are tied together with a rope over a frictionless pulley. Assume the table is frictionless and calculate:
a) the tension in the string.
b) the acceleration of the 3.00 kg mass.
27. Two objects, one of mass 1.00 kg and one of mass 1.50 kg are tied together over a frictionless pulley as in the diagram below. What is the acceleration of each mass and the tension in the string?
28. In a diagram similar to the one for question 27, a 4.50 kg mass is attached to a 7.50 kg mass. Determine the tension in the string and the accelerations of the masses.