Gravity - 6B/12.1 Physics 6B GRAVITY One more useful detail about gravity: The acceleration

Click here to load reader

download Gravity - 6B/12.1 Physics 6B   GRAVITY One more useful detail about gravity: The acceleration

of 35

  • date post

    29-Jun-2020
  • Category

    Documents

  • view

    0
  • download

    0

Embed Size (px)

Transcript of Gravity - 6B/12.1 Physics 6B GRAVITY One more useful detail about gravity: The acceleration

  • Gravity

    Physics 6B

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • GRAVITY

    Any pair of objects, anywhere in the universe, feel a mutual attraction due to gravity. There are no exceptions – if you have mass, every other mass is attracted to you, and you are attracted to every other mass. Look around the room – everybody here is attracted to you!

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • GRAVITY

    Any pair of objects, anywhere in the universe, feel a mutual attraction due to gravity. There are no exceptions – if you have mass, every other mass is attracted to you, and you are attracted to every other mass. Look around the room – everybody here is attracted to you!

    Newton’s Law of Universal Gravitation gives us a formula to calculate the attractive force between 2 objects:

    2 21

    grav r

    mm GF

    ⋅ =

    m1 and m2 are the masses, and r is the center-to-center distance between them

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

    m1 and m2 are the masses, and r is the center-to-center distance between them

    G is the gravitational constant – it’s tiny: G≈6.674*10-11 Nm2/kg2

    m1

    m2

    r

    F1 on 2

    F2 on 1

    Use this formula to find the magnitude of the gravity force.

    Use a diagram or common sense to find the direction. The force will always be toward the other mass.

  • GRAVITY

    Any pair of objects, anywhere in the universe, feel a mutual attraction due to gravity. There are no exceptions – if you have mass, every other mass is attracted to you, and you are attracted to every other mass. Look around the room – everybody here is attracted to you!

    Newton’s Law of Universal Gravitation gives us a formula to calculate the attractive force between 2 objects:

    2 21

    grav r

    mm GF

    ⋅ =

    m1 and m2 are the masses, and r is the center-to-center distance between them

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

    m1 and m2 are the masses, and r is the center-to-center distance between them

    G is the gravitational constant – it’s tiny: G≈6.674*10-11 Nm2/kg2

    m1

    m2

    r

    F1 on 2

    F2 on 1

    Use this formula to find the magnitude of the gravity force.

    Use a diagram or common sense to find the direction. The force will always be toward the other mass.

    *Note: If you are dealing with spherical objects with uniform density (our typical assumption) then you can pretend all the mass is concentrated at the center.

  • Example:

    Three planets are aligned as shown. The masses and distances are given in the diagram.

    Find the net gravitational force on planet H (the middle one).

    Planet Hollywood:Planet of the Apes: Daily Planet:

    1012 m 3 x 1012 m

    mass=6 x 1020 kgmass=6 x 1024 kg mass=3 x 1025 kg

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • Example:

    Three planets are aligned as shown. The masses and distances are given in the diagram.

    Find the net gravitational force on planet H (the middle one).

    Planet Hollywood:Planet of the Apes: Daily Planet:

    1012 m 3 x 1012 m

    FDP on HFApes on H

    mass=6 x 1020 kgmass=6 x 1024 kg mass=3 x 1025 kg

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • Example:

    Three planets are aligned as shown. The masses and distances are given in the diagram.

    Find the net gravitational force on planet H (the middle one).

    Planet Hollywood:Planet of the Apes: Daily Planet:

    1012 m 3 x 1012 m

    FDP on HFApes on H

    mass=6 x 1020 kgmass=6 x 1024 kg mass=3 x 1025 kg

    Our formula will find the forces (we supply the direction from looking at the diagram): 2

    21 grav

    r

    mm GF

    ⋅ =

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • Example:

    Three planets are aligned as shown. The masses and distances are given in the diagram.

    Find the net gravitational force on planet H (the middle one).

    Planet Hollywood:Planet of the Apes: Daily Planet:

    1012 m 3 x 1012 m

    FDP on HFApes on H

    mass=6 x 1020 kgmass=6 x 1024 kg mass=3 x 1025 kg

    Our formula will find the forces (we supply the direction from looking at the diagram): 2

    21 grav

    r

    mm GF

    ⋅ =

    ( )( ) ( )212

    2024

    kg Nm11

    HonApes m10

    kg106kg106 1067.6F 2

    2 ⋅⋅   

       ⋅−= − This is negative because

    the force points to the left

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • Example:

    Three planets are aligned as shown. The masses and distances are given in the diagram.

    Find the net gravitational force on planet H (the middle one).

    Planet Hollywood:Planet of the Apes: Daily Planet:

    1012 m 3 x 1012 m

    FDP on HFApes on H

    mass=6 x 1020 kgmass=6 x 1024 kg mass=3 x 1025 kg

    Our formula will find the forces (we supply the direction from looking at the diagram): 2

    21 grav

    r

    mm GF

    ⋅ =

    ( )( ) ( )

    N104.2 m10

    kg106kg106 1067.6F 11

    212

    2024

    kg Nm11

    HonApes 2 2

    ⋅−= ⋅⋅

     

      

     ⋅−= − This is negative because the force points to the left

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • Example:

    Three planets are aligned as shown. The masses and distances are given in the diagram.

    Find the net gravitational force on planet H (the middle one).

    Planet Hollywood:Planet of the Apes: Daily Planet:

    1012 m 3 x 1012 m

    FDP on HFApes on H

    mass=6 x 1020 kgmass=6 x 1024 kg mass=3 x 1025 kg

    Our formula will find the forces (we supply the direction from looking at the diagram): 2

    21 grav

    r

    mm GF

    ⋅ =

    ( )( ) ( )

    N104.2 m10

    kg106kg106 1067.6F 11

    212

    2024

    kg Nm11

    HonApes 2 2

    ⋅−= ⋅⋅

     

      

     ⋅−= − This is negative because the force points to the left

    ( )( ) ( )

    N103.1 m103

    kg106kg103 1067.6F 11

    212

    2025

    kg Nm11

    HonDP 2 2

    ⋅+= ⋅

    ⋅⋅  

      

     ⋅+= −

    This is positive because the force points to the right

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • Example:

    Three planets are aligned as shown. The masses and distances are given in the diagram.

    Find the net gravitational force on planet H (the middle one).

    Planet Hollywood:Planet of the Apes: Daily Planet:

    1012 m 3 x 1012 m

    FDP on HFApes on H

    mass=6 x 1020 kgmass=6 x 1024 kg mass=3 x 1025 kg

    Our formula will find the forces (we supply the direction from looking at the diagram): 2

    21 grav

    r

    mm GF

    ⋅ =

    ( )( ) ( )

    N104.2 m10

    kg106kg106 1067.6F 11

    212

    2024

    kg Nm11

    HonApes 2 2

    ⋅−= ⋅⋅

     

      

     ⋅−= − This is negative because the force points to the left

    ( )( ) ( )

    N103.1 m103

    kg106kg103 1067.6F 11

    212

    2025

    kg Nm11

    HonDP 2 2

    ⋅+= ⋅

    ⋅⋅  

      

     ⋅+= −

    This is positive because the force points to the right

    Add the forces to get the net force on H: N101.1F 11

    net ⋅−= Net force is to the left Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • GRAVITY One more useful detail about gravity:

    The acceleration due to gravity on the surface of a planet is right there in the formula.

    Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet.

    ( )2planet planet

    grav R

    mm GF

    ⋅ =

    Rplanet

    m

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • GRAVITY One more useful detail about gravity:

    The acceleration due to gravity on the surface of a planet is right there in the formula.

    Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet.

    ( )2planet planet

    grav R

    mm GF

    ⋅ =

    We already know that Fgrav is the weight of the

    Rplanet

    m

    We already know that Fgrav is the weight of the object, and that should just be mg (if the planet is the Earth)

    ( )2planet planet

    R

    mm Gmg

    ⋅ =

    Prepared by Vince Zaccone

    For Campus Learning Assistance Services at UCSB

  • GRAVITY One more useful detail about gravity:

    The acceleration due to gravity on the surface of a planet is right there in the formula.

    Here is the gravity formula, modified for the case where m