Centripetal Force Examples
Physics 6A
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Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Static friction is not strong enough to keep your tires from slipping on the pavement.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Static friction is not strong enough to keep your tires from slipping on the pavement.
OK, let’s say you are riding your bike around a level curve and your maximum speed is v when the radius
of the curve is R. Here are a couple of multiple choice questions:
1) What is your maximum speed if the radius of the curve is 2R?
v
a)
2
b)v
c ) 2v
d)2v
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Static friction is not strong enough to keep your tires from slipping on the pavement.
OK, let’s say you are riding your bike around a level curve and your maximum speed is v when the radius
of the curve is R. Here are a couple of multiple choice questions:
1) What is your maximum speed if the radius of the curve is 2R?
v
a)
We will need to find a formula relating v and R. A diagram may help.
2
b)v
c ) 2v
d)2v
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Static friction is not strong enough to keep your tires from slipping on the pavement.
OK, let’s say you are riding your bike around a level curve and your maximum speed is v when the radius
of the curve is R. Here are a couple of multiple choice questions:
1) What is your maximum speed if the radius of the curve is 2R?
v
a)
We will need to find a formula relating v and R. A diagram may help.
2
b)v
View from above
Notice that the friction force points toward the
c ) 2v
center of the curve. It is the centripetal force.
d)2v
friction
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Static friction is not strong enough to keep your tires from slipping on the pavement.
OK, let’s say you are riding your bike around a level curve and your maximum speed is v when the radius
of the curve is R. Here are a couple of multiple choice questions:
1) What is your maximum speed if the radius of the curve is 2R?
v
a)
We will need to find a formula relating v and R. A diagram may help.
2
b)v
View from above
Notice that the friction force points toward the
c ) 2v
center of the curve. It is the centripetal force.
d)2v
mv 2
friction =
R
friction
We know a formula for friction as well:
µsmg =
m(v max )2
R
Maximum static friction will give
maximum speed.
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Assistance Services at UCSB
Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Static friction is not strong enough to keep your tires from slipping on the pavement.
OK, let’s say you are riding your bike around a level curve and your maximum speed is v when the radius
of the curve is R. Here are a couple of multiple choice questions:
1) What is your maximum speed if the radius of the curve is 2R?
v
a)
We will need to find a formula relating v and R. A diagram may help.
2
b)v
View from above
Notice that the friction force points toward the
c ) 2v
center of the curve. It is the centripetal force.
d)2v
mv 2
friction =
R
friction
We know a formula for friction as well:
µsmg =
m(v max )2
R
vmax = µsgR
Maximum static friction will give
maximum speed.
Solve for vmax
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Assistance Services at UCSB
Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Static friction is not strong enough to keep your tires from slipping on the pavement.
OK, let’s say you are riding your bike around a level curve and your maximum speed is v when the radius
of the curve is R. Here are a couple of multiple choice questions:
1) What is your maximum speed if the radius of the curve is 2R?
v
a)
We will need to find a formula relating v and R. A diagram may help.
2
b)v
View from above
Notice that the friction force points toward the
c ) 2v
center of the curve. It is the centripetal force.
d)2v
mv 2
friction =
R
friction
We know a formula for friction as well:
µsmg =
m(v max )2
R
vmax = µsgR
Maximum static friction will give
maximum speed.
Solve for vmax
If R is doubled, vmax increases by √2
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Assistance Services at UCSB
Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Static friction is not strong enough to keep your tires from slipping on the pavement.
OK, let’s say you are riding your bike around a curve and your maximum speed is v when the radius of the
curve is R. Here are a couple of multiple choice questions:
1) What is your maximum speed if the radius of the curve is 2R?
v
a)
2
b)v
c ) 2v
d)2v
2) What is your maximum speed if the radius is R, but the road is wet, so that your coefficient of static
friction is only 1/3 of the value when the road is dry?
v
3
v
b)
3
a)
c ) 3v
d)3v
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Static friction is not strong enough to keep your tires from slipping on the pavement.
OK, let’s say you are riding your bike around a curve and your maximum speed is v when the radius of the
curve is R. Here are a couple of multiple choice questions:
1) What is your maximum speed if the radius of the curve is 2R?
v
a)
2
b)v
c ) 2v
d)2v
2) What is your maximum speed if the radius is R, but the road is wet, so that your coefficient of static
friction is only 1/3 of the value when the road is dry?
v
3
v
b)
3
a)
We can use our formula from part 1)
vmax = µsgR
c ) 3v
d)3v
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Ride your bike around a curve and you will notice that if you go too fast, your tires will slip and you will fall.
Why does this happen?
Static friction is not strong enough to keep your tires from slipping on the pavement.
OK, let’s say you are riding your bike around a curve and your maximum speed is v when the radius of the
curve is R. Here are a couple of multiple choice questions:
1) What is your maximum speed if the radius of the curve is 2R?
v
a)
2
b)v
c ) 2v
d)2v
2) What is your maximum speed if the radius is R, but the road is wet, so that your coefficient of static
friction is only 1/3 of the value when the road is dry?
v
3
v
b)
3
a)
We can use our formula from part 1)
vmax = µsgR
If µs decreases to µs/3 then vmax will decrease by √3.
c ) 3v
d)3v
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Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
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Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
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Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The normal force is the force of the wall pushing inward. This
is a centripetal force (it points toward the center of the circle).
friction
Normal
mg
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Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The normal force is the force of the wall pushing inward. This
is a centripetal force (it points toward the center of the circle).
We can write down our formula for centripetal force:
ΣFcent =
mv 2
N=
R
friction
mv 2
R
Normal
mg
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Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The vertical forces must balance out if the person wants to
avoid the crocodile pit, so we can write down a formula:
friction = mg
friction
What type of friction do we want – static or kinetic?
Normal
mg
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Assistance Services at UCSB
Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The vertical forces must balance out if the person wants to
avoid the crocodile pit, so we can write down a formula:
friction = mg
µs ⋅ N = mg
friction
By putting the maximum force of static
friction in our formula, we are assuming
the man is just on the verge of sliding.
Normal
mg
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Assistance Services at UCSB
Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The vertical forces must balance out if the person wants to
avoid the crocodile pit, so we can write down a formula:
friction = mg
µs ⋅ N = mg
mv 2
µs ⋅
= mg
R
friction
We can replace N with the
expression we found earlier.
Normal
mg
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Assistance Services at UCSB
Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The vertical forces must balance out if the person wants to
avoid the crocodile pit, so we can write down a formula:
friction = mg
µs ⋅ N = mg
friction
Normal
mv 2
µs ⋅
= mg
R
v2
µs ⋅
=g
R
mg
Now that we have this formula, how do we use it?
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Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The vertical forces must balance out if the person wants to
avoid the crocodile pit, so we can write down a formula:
friction = mg
µs ⋅ N = mg
friction
Normal
mv 2
µs ⋅
= mg
R
v2
µs ⋅
=g
R
gR
µs =
v2
mg
Notice that the mass canceled out, so based on the
given information we should solve for µ.
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Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The vertical forces must balance out if the person wants to
avoid the crocodile pit, so we can write down a formula:
friction = mg
µs ⋅ N = mg
mv 2
µs ⋅
= mg
R
v2
µs ⋅
=g
R
gR
The radius and speed are given, but the speed is in rpm,
µs =
so we will need to convert it to m/s.
v2
friction
Normal
mg
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Assistance Services at UCSB
Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The vertical forces must balance out if the person wants to
avoid the crocodile pit, so we can write down a formula:
friction = mg
µs ⋅ N = mg
friction
Normal
mv 2
µs ⋅
= mg
R
v2
µs ⋅
=g
R
gR
The radius and speed are given, but the speed is in rpm,
µs =
so we will need to convert it to m/s.
v2
mg
10rev 1min 2π ⋅ 20m
≈ 21 m
⋅
⋅
s
min 60 sec
rev
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Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The vertical forces must balance out if the person wants to
avoid the crocodile pit, so we can write down a formula:
friction = mg
µs ⋅ N = mg
mv 2
µs ⋅
= mg
R
v2
µs ⋅
=g
R
gR
Substitute the values for g, R and v
µs =
v2
 9.8 m (20m)


s2 

µ =
= 0.44
s
(21ms )2
friction
Normal
mg
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drops out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
We can start by drawing a free-body diagram of the forces on the person.
The vertical forces must balance out if the person wants to
avoid the crocodile pit, so we can write down a formula:
friction = mg
µs ⋅ N = mg
friction
Normal
mv 2
µs ⋅
= mg
R
v2
µs ⋅
=g
R
gR
µs =
v2
 9.8 m (20m)


s2 

µ =
= 0.44
s
(21ms )2
mg
So if the coefficient is 0.44 the
person will be on the verge of
sliding down into the pit.
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Wheel of Doom!
This carnival ride is a giant metal cylinder which will spin around and pin the occupants to the wall. The
fun part is when the floor drop out from below and the patrons see a spike-filled pit of angry crocodiles
awaiting them should they fall. As safety inspector, your problem will be to determine when it will be
unsafe to ride. The given information is this: Radius of cylinder = 20m. Speed of rotation = 10 rpm.
a) Will leather-clad Biker Bob (mass = 100kg ;coeff. of static friction = 0.6) be safe?
b) How about Disco Stu, a 75kg man wearing a silk shirt and polyester pants (µs=0.15)?
Biker Bob is safe (his 0.6 coefficient
is larger than 0.44 , so static friction
is enough to hold him in place)
friction
Disco Stu is doomed! (his 0.15
coefficient is too small, so static
friction fails to hold him in place)
Normal
mg
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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!
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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 gravitation gives us a formula to calculate the attractive force between 2 objects:
Fgrav = G
m1 ⋅ m2
r2
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
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.
m2
m1
r
F2 on 1
F1 on 2
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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).
1012 m
3 x 1012 m
Planet of the Apes:
Planet Hollywood:
Daily Planet:
mass=6 x 1024 kg
mass=6 x 1020 kg
mass=3 x 1025 kg
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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).
1012 m
3 x 1012 m
Planet of the Apes:
Planet Hollywood:
Daily Planet:
mass=6 x 1024 kg
mass=6 x 1020 kg
mass=3 x 1025 kg
We should start by defining our coordinate system.
Let’s put the origin at planet H and say positive is to the right.
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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).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
Planet Hollywood:
Daily Planet:
mass=6 x 1024 kg
mass=6 x 1020 kg
mass=3 x 1025 kg
We can also draw the forces on planet H in our diagram.
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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).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
Planet Hollywood:
Daily Planet:
mass=6 x 1024 kg
mass=6 x 1020 kg
mass=3 x 1025 kg
Our formula will find the forces (we supply the
direction from looking at the diagram):
m ⋅m
Fgrav = G 1 2
r2
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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).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
Planet Hollywood:
Daily Planet:
mass=6 x 1024 kg
mass=6 x 1020 kg
mass=3 x 1025 kg
m ⋅m
Fgrav = G 1 2
r2
Our formula will find the forces (we supply the
direction from looking at the diagram):
(
)(
24
20

−11 Nm2  6 ⋅ 10 kg 6 ⋅ 10 kg
FApes on H = − 6.67 ⋅ 10

2 
2
kg


1012 m
(
)
)
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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).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
Planet Hollywood:
Daily Planet:
mass=6 x 1024 kg
mass=6 x 1020 kg
mass=3 x 1025 kg
m ⋅m
Fgrav = G 1 2
r2
Our formula will find the forces (we supply the
direction from looking at the diagram):
(
)(
)
24
20

−11 Nm2  6 ⋅ 10 kg 6 ⋅ 10 kg
= −2.4 ⋅ 1011N
FApes on H = − 6.67 ⋅ 10

2 
2
kg 

1012 m
(
)
This is negative because the
force points to the left
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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).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
Planet Hollywood:
Daily Planet:
mass=6 x 1024 kg
mass=6 x 1020 kg
mass=3 x 1025 kg
m ⋅m
Fgrav = G 1 2
r2
Our formula will find the forces (we supply the
direction from looking at the diagram):
(
)(
)
24
20

−11 Nm2  6 ⋅ 10 kg 6 ⋅ 10 kg
= −2.4 ⋅ 1011N
FApes on H = − 6.67 ⋅ 10

2 
2
kg 

1012 m
(
(
)
)(
)
25
20

−11 Nm2  3 ⋅ 10 kg 6 ⋅ 10 kg
FDP on H = + 6.67 ⋅ 10
= +1.3 ⋅ 1011N

2 
2
kg 

3 ⋅ 1012 m
(
)
This is negative because the
force points to the left
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).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
Planet Hollywood:
Daily Planet:
mass=6 x 1024 kg
mass=6 x 1020 kg
mass=3 x 1025 kg
m ⋅m
Fgrav = G 1 2
r2
Our formula will find the forces (we supply the
direction from looking at the diagram):
(
)(
)
24
20

−11 Nm2  6 ⋅ 10 kg 6 ⋅ 10 kg
= −2.4 ⋅ 1011N
FApes on H = − 6.67 ⋅ 10

2 
2
kg 

1012 m
(
(
)
)(
)
25
20

−11 Nm2  3 ⋅ 10 kg 6 ⋅ 10 kg
FDP on H = + 6.67 ⋅ 10
= +1.3 ⋅ 1011N

2 
2
kg 

3 ⋅ 1012 m
(
Add the forces to get the net force on H:
)
11
Fnet = −1.1⋅ 10 N
This is negative because the
force points to the left
This is positive because the
force points to the right
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.
Fgrav = G
mplanet ⋅ m
(Rplanet )2
m2
Rplanet
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.
Fgrav = G
mplanet ⋅ m
(Rplanet )2
We already know that Fgrav is the weight of the object,
and that should just be mg (if the planet is the Earth)
m2
Rplanet
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.
Fgrav = G
mplanet ⋅ m
(Rplanet )2
We already know that Fgrav is the weight of the object,
and that should just be mg (if the planet is the Earth)
mg = G
mplanet ⋅ m
2
(Rplanet )
m
Rplanet
This part is g
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB