Newton s 2 nd Law of Motion Physics 3 rd /4th 6wks Updated as of 12/17/15
Newton s 2 nd Law: Football Correlation
Newton s 2 nd Law of Motion What is the difference between tossing a ball and throwing it as hard as you can? The greater the force, the greater its acceleration will be. If you throw both a tennis ball and a bowling ball as hard as you can, why won t they accelerate at the same rates or have the same speed? The acceleration of an object depends upon its mass as well as the force exerted upon it. Newton s 2 nd Law of Motion describes how mass, force and acceleration are connected.
The law states: the acceleration of an object is related to the relationship between the net force acting upon it and its mass. The law states: if an unbalanced force acts on a body, that body will experience acceleration Also known as the Law of Acceleration Acceleration and the Net Force that an object experiences are directly correlated. There is an inverse relationship between an object s mass & the acceleration it experiences when a force is applied to it. The more massive something is, the harder it is to push and vice versa.
The SI unit for force is the Newton The symbol for the Newton is N The Net Force an object is experiencing can also be calculated by the formula to the right. 1 Newton = 0.225 Pounds. 1 Pound = 4.44 N A Newton is the amount of force required To accelerate 1 kg of mass, 1 m/s 2 Constant: At the Earth s surface, an Object that has a mass of 1 kg has a weight of 9.8 N Therefore: 1 kg = 2.2 lbs. 1N = 0.225 Pounds
2 nd Law in a nutshell A = F / M A= F / M According to the Second Law of Motion, when fired a bullet will experience a greater acceleration than the gun, because of its smaller mass
Force, Mass, & Acceleration F M A Note: three units are usually linked Mass = kg Acceleration = m/s 2 Force = N
Example Problem #1: finding net force If a rock had a mass of 3.2 kg and was accelerating at a rate of 0.65 m/s 2, what net force was it experiencing? F = 3.2 kg 0.65 m/s 2 F = 2.08 kg m/s 2 Note: N = kg m/s 2 F = 2.08 N
Example Problem #2: finding acceleration If the net force on an object was 75 N and the mass of the object was 12 kg, what was its acceleration? a = F M Note: N = kg m/s 2 a = a = 75 N 12 kg 75 kg m/s2 12 kg a = 6.25 m/s 2
Example #3: Calculating acceleration after finding net force If F 1 = 40 N and F 2 = 15 N and the mass of the object was 10 kg, what was the box acceleration? 10 kg F 2 = 15 N F 1 = 40 N Note: N = kg m/s 2 a = F M a = a = a = (40 N 15 N) 10 kg 25 N 10 kg 25 kg m/s2 10 kg a = 2.5 m/s 2 right Remember: Force is a vector, so in this 1-D problem, + means right
Example Problem #4: finding mass If the Net Force was 5 N and the acceleration was 2 m/s 2, what was the mass of the object? m = F a m = 5 N 2 m/s 2 m = 5 kg m/s2 2 m/s 2 m = 2.5 kg
Mass vs. Weight Mass the quantity of matter in an object. Mass measures the inertia (from the Latin for laziness )that an object exhibits in response to any effort made to start it, stop it, or otherwise change its current motion.
Mass vs. Weight Weight the force of gravity on an object. While mass and weight are not the same, they are directly proportional. Objects with more mass weigh more. Remember: mass has to do with how much matter is in an object, while weight has to do with how strongly that matter is attracted by gravity. Therefore, your weight will vary with gravitational attraction, while your mass will be the same wherever you are in the Universe.
Calculating the Force of Gravity or Weight The gravitational attraction of the Earth causes all objects to have an acceleration of 9.8 m/s 2 (often rounded to 10 m/s 2 for estimation) In the SI system, weight is correctly measured in Newtons (as opposed to pounds in the English system) The gravitational force on an object is the same as its weight. With the 2 nd Law formula, weight is calculated by Remember, when we refer to weight we mean the magnitude of the force of gravity so Weight = F gravity F gravity = m x g F gravity = m x 9.8 m/s 2
Example Problem #5: finding weight Carlos the Space Squirrel stepped out from his space capsule on the Planet of Acorn. If the acceleration due to gravity on the planet were 17 m/s 2, and his mass was 7 kg, what did he weigh when he was on the planet? F = 7 kg 17 m/s 2 F = 119 kg m/s 2 Note: N = kg m/s 2 F = 119 N
Gravitational Acceleration Law of Gravitation states: any 2 masses exert an attractive force upon each other. The attractive force depends upon the mass of the 2 objects and the distances between them. The force of gravity between two objects increases as mass increases. The force of gravity also increases as objects move closer together. Gravity is a long range force even stars pull upon you a little the long range force of gravity is what helps to give the universe its form.
Calculating the force of Gravitational Attraction between any two objects FYI: the value of the constant was discovered by the British scientist Henry Cavendish a century after Newton s death
Example Problem # 6 Jack stands 2 m from Jill. Jack has a mass of 50 kg and Jill has a mass of 40 kg. What is the force of gravitational attraction between them? Given M 1 = 50 kg M 2 = 40 kg D = 2 m F g = 6.67 x 10-11 N m2 kg 2 50 kg 40 kg (2m)2 F g = 6.67 x 10-11 N m2 2000 kg 2 kg 2 4m 2 F g = 6.67 x 10-11 N m2 kg 2 500 kg2 m 2 F g = 3.335 x 10-8 N
Free Fall: Speed Gravity an attractive field of force that exists around every mass Free Fall motion under the influence of gravity only The acceleration of an object falling on the Earth, when air resistance is negligible is approximately 10 m/s 2 (or when you are being more exact, the value used is 9.8 m/s 2 ). g is used to represent the acceleration due to gravity on the Earth. g = 9.8 m/s 2 Instantaneous speed of an object in free fall = acceleration due to gravity x time v = gt
Free Fall and Mass An object in free-fall, that is with only the force of gravity acting upon it, will fall with the same acceleration as every other object in free-fall. If there is another force acting upon it, say the force of air resistance the acceleration may differ, as air resistance works less on more massive items than on less massive ones.
Exploring falling objects
Falling Objects 2
Apollo 15 (August 6, 1971) a feather and a hammer dropped at the same time
What is the difference between Mass and Weight?
Free Fall When an object is thrown straight up, it slows from its initial velocity to zero velocity. The object is accelerating, because its velocity is changing. The speed decreases at the same rate going upwards that it increases at going downwards in free fall, which is at 9.8 m/s 2 or approximately 10 m/s 2 Note: when moving away from the Earth g is a negative value since it acts against the object and it is positive when the object is moving towards the Earth
Free Fall: Distance For free falling objects, the distance an object falls Can be found by the following equation: d = ½ g t 2 g = acceleration due to gravity t = time
Free Fall: Speed vs. Time Graph Note: there is a linear or direct relationship between the time an object falls and its speed. The relationship exists for objects thrown straight up as well.
Free Fall: Distance vs. Time Graph Note: the relationship between the time a freely falling object moves versus the distance it has traveled is parabolic. If the object were thrown straight up, this would still be true.
Key Formulas V f = V i + at V i = V f - at T = (vf v i) g For items dropped from rest, where v i = 0 the following can be used: v = gt d = ½ g t 2 T = 2d g
Velocity if Acceleration and time are known V f = V i + at An object s velocity is equal to its initial velocity (V i ) plus the product of its acceleration and the time it has traveled.
Example #7 A ball is dropped from a high balcony. How fast is it moving after 4 seconds (disregarding air resistance)? Given Info *Note: in free fall, the initial speed is zero, so V i = 0 a= g = 9.8 m/s 2 A constant t= 4 seconds V f = V i + at V f = 0 + (9.8 m/s 2 )(4 sec) V f = 9.8 m/s sec V f = 39.2 m/s 4 sec 1
Example #8 A toy car was traveling at an initial velocity of 2.4 m/s. How fast is it moving after 3 seconds if it undergoes a uniform acceleration of 1.4 m/s 2? Given Info V i = 2.4 m/s a= 1.4 m/s 2 V f = V i + at t= 3 seconds V f = 2.4 m/s + (1.4 m/s 2 )(3 sec) V f = 2.4 m/s + 1.4 m/s sec 3 sec 1 V f = 2.4 m/s + 4.2 m/s V f = 6.6 m/s
Example #9 A ball was thrown up into the air at an initial velocity of 26.8 m/s. How fast was it moving 2 seconds later? Given Info V i = 26.8 m/s a= -9.8 m/s 2 t= 2 seconds V f = V i + at V f = 26.8 m/s + (-9.8 m/s 2 )(2 sec) V f = 26.8 m/s + 9.8 m/s sec 2 sec 1 V f = 26.8 m/s +(- 19.6 m/s) V f = 7.2 m/s
The STAAR Reference Materials formula and its use
Example #10 An apple falls from a tree. If it takes 2 seconds for it to hit the ground, how high is the point from which the apple fell? Given Info *Note: in free fall, the initial speed is zero, so V i = 0 t= 2 seconds a= g = 9.8 m/s 2 A constant d = (0)(2sec) + 0.5(9.8 m/s 2 )(2 sec) 2 d = 0 + (4.9 m/s 2 )(4 sec 2 ) d = 4.9 m sec 2 4 sec2 1 d = 19.6 m
Example #11 An apple falls from rest. How far has it fallen in 3 seconds? Given Info *Note: in free fall, the initial speed is zero, so V i = 0 t= 3 seconds a= g = 9.8 m/s 2 A constant d = (0)(3 sec) + 0.5(9.8 m/s 2 )(3 sec) 2 d = 0 + (4.9 m/s 2 )(9 sec 2 ) d = 4.9 m sec 2 9 sec2 1 d = 44.1 m
Example #12 An object moves with an initial velocity of 2 m/s for 3 seconds while accelerating at 1 m/s 2. How far has the object traveled? Given Info V i = 2 m/s t= 3 seconds d = (2 m/s)(3 sec) + 0.5(1 m/s 2 )(3 sec) 2 a= 1 m/s 2 2 m d = + 0.5 1 m/s 2 3 sec 2 s 3 s 1 d = 6 m + 0.5 m sec 2 d = 6 m + 4.5 m 9 sec2 1 d = 10.5 m
Example 13: finding Time from Velocity & g Timothy drops an egg out of a helicopter. By the time the egg hits the ground, it has a velocity of 24.5 m/s downward. (Let g = 9.8 m/s 2 ) How long is the fall-time of the egg? Given Info V i = 0 m/s (since it was dropped from rest) V = 24.5 m/s g= 9.8 m/s 2 T = (vf v i) g T = T = (24.5 m/s 0) T = 2.5 s 9.8 m/s 2 24.5 m/s 9.8 m/s 2 note: the two m/s cancel each other leaving the seconds remaining as the unit *time is never a negative value
Example 14: finding Time from Velocity & g Jo Bob threw a marble up into the air at a velocity of 34 m/s. How long did it take for the marble to reach its highest point (where its velocity would be 0 m/s)? Given Info V i = 34 m/s (since it was dropped from rest) V f = 0 m/s g= - 9.8 m/s 2 T = (vf v i) g T = T = (0 34 m/s) 9.8 m/s 2 34 m/s 9.8 m/s 2 T 3.47 s note: the two m/s cancel each other leaving the seconds remaining as the unit *time is never a negative value
Example 15: finding Time from distance & g When eating breakfast at the Eiffel Tower while on vacation, Job Bob dropped his delicious buttered croissant. According to the guidebook, the Eiffel Tower has a height of 300 m from the restaurant. How many seconds did it take for the croissant to hit someone out for their morning stroll? Given Info T = 2d g d = 300 m g= 9.8 m/s 2 T = T = 2 x 300 m 9.8 m/s 2 600 m 9.8 m/s 2 T = 61. 22 s 2 T 7. 8 sec note: the two meters will cancel each other out leaving the seconds remaining as the unit *time is never a negative value
Example 15: finding Time from distance & g When eating breakfast at the Eiffel Tower while on vacation, Job Bob dropped his delicious buttered croissant. According to the guidebook, the Eiffel Tower has a height of 300 m from the restaurant. How many seconds did it take for the croissant to hit someone out for their morning stroll? Given Info T = 2d g d = 300 m g= 9.8 m/s 2 T = T = 2 x 300 m 9.8 m/s 2 600 m 9.8 m/s 2 T = 61. 22 s 2 T 7. 8 sec note: the two meters will cancel each other out leaving the seconds remaining as the unit *time is never a negative value
Free Fall, Air Resistance, and Terminal Velocity Gravity causes all objects to accelerate same in free fall. On Earth, this acceleration value is 9.8 m/s/s. (also known as g) Falling objects initially accelerate because there isn t a force large enough to balance out the downward force of gravity. As objects plow through the air they encounter resistance which slows them down. The amount of air resistance is directly related to the ratio of the surface area of an object versus its mass.
Free Fall, Air Resistance, and Terminal Velocity Recall that regardless of their mass all objects free-fall at the same rate (10 m/s2) on Earth. But when falling in air, the force of it will act to slow an object down. An object will continue to accelerate until the upward force of air resistance is equal to the downward force of gravity. Terminal velocity is when the force of air resistance is equal to the force of gravity on an object. At that point, the object then has an acceleration of zero and the object falls at a constant speed.
Air Resistance A Freely Falling Body is an object that is influenced by the force of gravity alone. Air Resistance (also known as Air Friction) is the force that resists objects falling through the air. Air Resistance not mass affects the fall of objects, otherwise (like in a vacuum) all objects fall at the same rate. Air resistance is also known as drag.
Terminal Velocity The more massive an object the more inertia it has. It takes a greater amount of force to balance out the downward force of gravity, ergo the more massive an object, the longer it will fall before reaching terminal velocity. The greater the surface area of an object, the more air an object encounters. Therefore, greater surface area = lower terminal velocity
Terminal Velocity Diagram D shows the man after reaching terminal velocity since the force of gravity is balanced by force of air resistance and acceleration is zero
Terminal Velocity and Air Resistance With Air Resistance No air resistance