Gravity and Free Fall BJU Press Art baseball: Physical Science text p. 105

Gravity Gravitational attraction between all objects is a basic property of all matter. So why do all objects in the universe not come together in one lump? BJU Press Art baseball: Physical Science text p. 105

Gravity The force of gravity on small objects is not great enough to overcome friction. The force of gravity for large objects, like stars, is very weak because of the great distances between them. BJU Press Art baseball: Physical Science text p. 105

Gravity Newton studied gravity and came up with an equation for the force of gravity based on just three variables. The variables are the masses of the two objects and the distance between the centers of the objects’ masses. BJU Press Art baseball: Physical Science text p. 105

gravitational constant distance between centers of mass (m) The Law of Universal Gravitation mass of larger object Mm Fg = G mass of smaller object r2 force of gravity (N) gravitational constant distance between centers of mass (m) BJU Press Art baseball: Physical Science text p. 105

Gravity He could not use the equation because he did not know the value for G. Its value was found to be 6.67 × 10-11 N•m2/kg2. The units are necessary so that the answer is in newtons. The small size of the number shows that gravity is very weak. BJU Press Art baseball: Physical Science text p. 105

What does this equation tell us? Gravity What does this equation tell us? The force of gravity is directly proportional to each mass. The force of gravity is inversely proportional to distance squared. Fg = G Mm r2 BJU Press Art baseball: Physical Science text p. 105

Sample Problem 1 Find the force of gravity between two 5000 kg masses whose centers are 5 meters apart. Fg = G Mm r2 6.67×10-11 × 5000 kg × 5000 kg Fg = (5 m)2 Fg = 6.67 × 10-5 N

Sample Problem 2 What is the force you would feel if you were standing on Ceres, the largest asteroid in the solar system? Mass of Ceres = 8.7×1020 kg Your mass w/ spacesuit = 136 kg Radius of Ceres = 473,000 m

Sample Problem 2 Mm Fg = G r2 6.67×10-11 × 8.7×1020 kg × 136 kg Fg = Fg = 35.3 N

Sample Problem 3 Find the force of gravity between the earth and the moon. Mass of earth = 5.98×1024 kg Mass of moon = 7.35×1022 kg Distance between centers of earth and moon = 3.84×108 m

Sample Problem 3 Mm Fg = G r2 6.67×10-11 × 5.98×1024 kg × 7.35×1022 kg Fg = 1.99×1020 N

Does a heavier body fall faster than a lighter one? Free Fall Does a heavier body fall faster than a lighter one? Aristotle thought so, and he was a great Greek thinker, so he must have been correct. BJU Press Art baseball: Physical Science text p. 105

Free Fall Galileo’s “thought experiment” disproved Aristotle, but most scientists did not listen to him. But if Galileo is right, why does a piece of paper fall slower than a pen? BJU Press Art baseball: Physical Science text p. 105

It is not the mass of the pen that makes it fall faster. Free Fall It is not the mass of the pen that makes it fall faster. Rather, it is the air resistance on the paper that slows the paper down. Wad up the paper and it falls as fast as the pen. BJU Press Art baseball: Physical Science text p. 105

Free Fall The rate of fall is controlled by the ratio of the object’s weight to its surface area. BJU Press Art baseball: Physical Science text p. 105

David Scott – Apollo 15 mission

No, as the velocity increases, so does air resistance. Free Fall Does gravity keep accelerating an object faster and faster without limit? No, as the velocity increases, so does air resistance. BJU Press Art baseball: Physical Science text p. 105

It has reached terminal velocity. Free Fall When the force of air resistance = gravity’s force, the object doesn’t fall any faster because the forces are balanced. It has reached terminal velocity. BJU Press Art baseball: Physical Science text p. 105

Free Fall When an object falls with only gravity acting on it, it is said to be in free fall. BJU Press Art baseball: Physical Science text p. 105

If an object falls in a vacuum, there is no terminal velocity. Free Fall Free fall cannot happen if the object falls in an atmosphere because moving through the air produces air resistance or drag. If an object falls in a vacuum, there is no terminal velocity. BJU Press Art baseball: Physical Science text p. 105

Gravity and Weight Weight is the force caused by the earth’s gravity. Since F = ma, if we know the weight of an object (a = 9.8 m/s2 on the earth), we can calculate its mass by dividing its weight by “a.” BJU Press Art baseball: Physical Science text p. 105

Gravity and Weight Remember ... Mass is the unit of measure for the amount of a substance and is measured with a balance. Weight is a force and must be measured with a scale. It changes with the acceleration due to gravity. BJU Press Art baseball: Physical Science text p. 105

acceleration due to gravity = 9.81 m/s2 Gravity and Weight Another way to write the F = ma equation is: w = mg acceleration due to gravity = 9.81 m/s2 weight (N) mass (kg) BJU Press Art baseball: Physical Science text p. 105

Sample Problem 4 How much does a 1 kg mass weigh? w = mg w = 1 kg × 9.81 m/s2 w = 9.81 N BJU Press Art baseball: Physical Science text p. 105

acceleration due to gravity = 9.81 m/s2 Free Fall and Distance To find the velocity of an object in free fall use: v = g(Δt) time it falls (s) velocity (m/s) acceleration due to gravity = 9.81 m/s2 BJU Press Art baseball: Physical Science text p. 105

“Free Fall” implies that the object is dropped, not thrown downward Sample Problem 5 How fast is an object traveling after 1.0 s in free fall? v = g(Δt) v = (9.81 m/s2)(1.0 s) v = 9.81 m/s “Free Fall” implies that the object is dropped, not thrown downward

Sample Problem 6 How fast is an object traveling after 2.0 s in free fall? v = g(Δt) v = (9.81 m/s2)(2.0 s) v = 19.62 m/s

Free Fall Data Time (s) Velocity (m/s) 1 9.81 2 19.62 3 29.43 4 39.24 1 9.81 2 19.62 3 29.43 4 39.24 39.24 4 29.43 3 19.62 2 9.81 1 Velocity (m/s) Time (s) BJU Press Art baseball: Physical Science text p. 105

Free Fall and Distance Note that the earth’s gravity is always 9.81 m/s2 near the earth. This means that an object in free fall experiences uniform acceleration. BJU Press Art baseball: Physical Science text p. 105

1 g(Δt)2 d = 2 Free Fall and Distance The hang time equation: distance an object falls (m) time an object falls (s) acceleration due to gravity = 9.81 m/s2 BJU Press Art baseball: Physical Science text p. 105

Sample Problem 7 How far does an object fall in free fall after 1.0 seconds? d = g(Δt)2 1 2 d = (9.81 m/s2)(1.0 s)2 1 2 d = (9.81 m/s2)(1.0 s2) 1 2 d = 4.91 m

Free Fall Data Time (s) Speed (m/s) Distance (m) 1 9.81 4.91 2 19.62 3 1 9.81 4.91 2 19.62 3 29.43 44.15 4 39.24 78.48 Time (s) Speed (m/s) Distance (m) 1 9.81 4.91 2 19.62 3 29.43 44.15 4 39.24 78.48 BJU Press Art baseball: Physical Science text p. 105

Sample Problem 8 How far does an object fall in free fall after 2.0 seconds? d = g(Δt)2 1 2 d = (9.81 m/s2)(2.0 s)2 1 2 d = (9.81 m/s2)(4.0 s2) 1 2 d = 19.62 m

T/F All objects experience gravitational attraction. True

Find the force of gravity between two 9,362 kg tractor trailers that are 3.68 m apart.

Find the force of gravity between two 9,362 kg tractor trailers that are 3.68 m apart. Fg = G Mm r2 6.67×10-11 × 9362 kg × 9362 kg Fg = (3.68 m)2 Fg = 4.32 × 10-4 N

Saturn has a mass of 5. 6846 × 1026 kg and Jupiter has a mass of 1 Saturn has a mass of 5.6846 × 1026 kg and Jupiter has a mass of 1.899 × 1027 kg. At their closest point, they are 6.493 × 108 km apart. What is the force of gravity between Saturn and Jupiter at their closest point? 2.56×1036 N 1.71×1020 N 1.71×1026 N 1.66×1045 N

Wait! The distance must be in meters. Mass of Saturn = 5.6846 × 1026 kg Mass of Jupiter = 1.899 × 1027 kg Distance = 6.493 × 108 km Fg = G Mm r2 Wait! The distance must be in meters. 6.67×10-11 × 5.6846×1026 kg × 1.899×1027 kg Fg = (6.493×108 km)2 (6.493×1011 m)2 Fg = 1.71 × 1020 N

What falls faster in a vacuum? 100 kg bowling ball 10 kg bowling ball They would fall at the same speed.

How fast is an object traveling after 8.0 s in free fall? 78.48 m/s 64.00 m/s 769.89 m/s 32.00 mph

How fast is an object traveling after 8.0 s in free fall? v = g(Δt) v = (9.81 m/s2)(8.0 s) v = 78.48 m/s

How far does an object fall after 8.0 s in free fall? 39.24 m 627.84 m 3,079.56 m 313.92 m

How far does an object fall after 8.0 s in free fall? g(Δt)2 1 2 d = (9.81 m/s2)(8.0 s)2 1 2 d = 313.92 m