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Centripetal Force Examples
Physics 6A
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
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?
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
v2)d
v2)c
v)b2
v)a
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?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We will need to find a formula relating v and R. A diagram may help.
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?
v2)d
v2)c
v)b2
v)a
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We will need to find a formula relating v and R. A diagram may help.
friction
View from aboveNotice that the friction force points toward the center of the curve. It is the centripetal force.
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?
v2)d
v2)c
v)b2
v)a
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?We will need to find a formula relating v and R. A diagram may help.
friction
View from aboveNotice that the friction force points toward the center of the curve. It is the centripetal force.
R
mvfriction
2
We know a formula for friction as well:
R
vmmg
2max
s Maximum static friction will give maximum speed.
v2)d
v2)c
v)b2
v)a
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?We will need to find a formula relating v and R. A diagram may help.
friction
View from aboveNotice that the friction force points toward the center of the curve. It is the centripetal force.
R
mvfriction
2
We know a formula for friction as well:
R
vmmg
2max
s Maximum static friction will give maximum speed.
gRv smax Solve for vmax
v2)d
v2)c
v)b2
v)a
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?We will need to find a formula relating v and R. A diagram may help.
friction
View from aboveNotice that the friction force points toward the center of the curve. It is the centripetal force.
R
mvfriction
2
We know a formula for friction as well:
R
vmmg
2max
s Maximum static friction will give maximum speed.
gRv smax Solve for vmax
If R is doubled, vmax increases by √2
v2)d
v2)c
v)b2
v)a
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?
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?
v3)d
v3)c
3
v)b
3
v)a
v2)d
v2)c
v)b2
v)a
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?
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?
v3)d
v3)c
3
v)b
3
v)a
v2)d
v2)c
v)b2
v)a
We can use our formula from part 1) gRv smax
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?
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?
v3)d
v3)c
3
v)b
3
v)a
v2)d
v2)c
v)b2
v)a
We can use our formula from part 1) gRv smax
If µs decreases to µs/3 then vmax will decrease by √3.
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
The normal force is the force of the wall pushing inward. This is a centripetal force (it points toward the center of the circle).
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
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:
R
mvN
R
mvF
2
2
cent
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
The vertical forces must balance out if the person wants to avoid the crocodile pit, so we can write down a formula:
mgfriction
What type of friction do we want – static or kinetic?
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
The vertical forces must balance out if the person wants to avoid the crocodile pit, so we can write down a formula:
mgN
mgfriction
s
By putting the maximum force of static friction in our formula, we are assuming the man is just on the verge of sliding.
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
The vertical forces must balance out if the person wants to avoid the crocodile pit, so we can write down a formula:
mgR
mv
mgN
mgfriction
2
s
s
We can replace N with the expression we found earlier.
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
The vertical forces must balance out if the person wants to avoid the crocodile pit, so we can write down a formula:
gR
v
mgR
mv
mgN
mgfriction
2
s
2
s
s
Now that we have this formula, how do we use it?
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
The vertical forces must balance out if the person wants to avoid the crocodile pit, so we can write down a formula:
2s
2
s
2
s
s
v
gR
gR
v
mgR
mv
mgN
mgfriction
Notice that the mass canceled out, so based on the given information we should solve for µ.
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
The vertical forces must balance out if the person wants to avoid the crocodile pit, so we can write down a formula:
2s
2
s
2
s
s
v
gR
gR
v
mgR
mv
mgN
mgfriction
The radius and speed are given, but the speed is in rpm, so we will need to convert it to m/s.
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
The vertical forces must balance out if the person wants to avoid the crocodile pit, so we can write down a formula:
2s
2
s
2
s
s
v
gR
gR
v
mgR
mv
mgN
mgfriction
The radius and speed are given, but the speed is in rpm, so we will need to convert it to m/s.
sm21
rev
m202
sec60
min1
min
rev10
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
The vertical forces must balance out if the person wants to avoid the crocodile pit, so we can write down a formula:
44.0
21
m208.9
v
gR
gR
v
mgR
mv
mgN
mgfriction
2
sm
sm
s
2s
2
s
2
s
s
2
Substitute the values for g, R and v
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)?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
We can start by drawing a free-body diagram of the forces on the person.
mg
Normal
friction
The vertical forces must balance out if the person wants to avoid the crocodile pit, so we can write down a formula:
44.0
21
m208.9
v
gR
gR
v
mgR
mv
mgN
mgfriction
2
sm
sm
s
2s
2
s
2
s
s
2
So if the coefficient is 0.44 the person will be on the verge of sliding down into the pit.
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)?
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 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)?
mg
Normal
friction
Biker Bob is safe (his 0.6 coefficient is larger than 0.44 , so static friction is enough to hold him in place)
Disco Stu is doomed! (his 0.15 coefficient is too small, so static friction fails to hold him in place)
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 gravitation gives us a formula to calculate the attractive force between 2 objects:
221
gravr
mmGF
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.
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:
mass=6 x 1020 kg
Planet of the Apes:
mass=6 x 1024 kg
Daily Planet:
mass=3 x 1025 kg
1012 m 3 x 1012 m
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:
mass=6 x 1020 kg
Planet of the Apes:
mass=6 x 1024 kg
Daily Planet:
mass=3 x 1025 kg
1012 m 3 x 1012 m
We should start by defining our coordinate system.
Let’s put the origin at planet H and say positive is 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:
mass=6 x 1020 kg
Planet of the Apes:
mass=6 x 1024 kg
Daily Planet:
mass=3 x 1025 kg
1012 m 3 x 1012 m
We can also draw the forces on planet H in our diagram.
FDP on HFApes on H
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:
mass=6 x 1020 kg
Planet of the Apes:
mass=6 x 1024 kg
Daily Planet:
mass=3 x 1025 kg
1012 m 3 x 1012 m
FDP on HFApes on H
221
gravr
mmGF
Our formula will find the forces (we supply the
direction from looking at the diagram):
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:
mass=6 x 1020 kg
Planet of the Apes:
mass=6 x 1024 kg
Daily Planet:
mass=3 x 1025 kg
1012 m 3 x 1012 m
FDP on HFApes on H
221
gravr
mmGF
212
2024
kgNm11
HonApesm10
kg106kg1061067.6F
2
2
Our formula will find the forces (we supply the direction from looking at the diagram):
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:
mass=6 x 1020 kg
Planet of the Apes:
mass=6 x 1024 kg
Daily Planet:
mass=3 x 1025 kg
1012 m 3 x 1012 m
Our formula will find the forces (we supply the direction from looking at the diagram):
FDP on HFApes on H
221
gravr
mmGF
N104.2m10
kg106kg1061067.6F 11
212
2024
kgNm11
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:
mass=6 x 1020 kg
Planet of the Apes:
mass=6 x 1024 kg
Daily Planet:
mass=3 x 1025 kg
1012 m 3 x 1012 m
Our formula will find the forces (we supply the direction from looking at the diagram):
FDP on HFApes on H
221
gravr
mmGF
N104.2m10
kg106kg1061067.6F 11
212
2024
kgNm11
HonApes 2
2
This is negative because the
force points to the left
N103.1m103
kg106kg1031067.6F 11
212
2025
kgNm11
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:
mass=6 x 1020 kg
Planet of the Apes:
mass=6 x 1024 kg
Daily Planet:
mass=3 x 1025 kg
1012 m 3 x 1012 m
Our formula will find the forces (we supply the direction from looking at the diagram):
FDP on HFApes on H
221
gravr
mmGF
N104.2m10
kg106kg1061067.6F 11
212
2024
kgNm11
HonApes 2
2
This is negative because the
force points to the left
N103.1m103
kg106kg1031067.6F 11
212
2025
kgNm11
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 11net
Net force is to the left
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
2planet
planetgrav
R
mmGF
Rplanet
m
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.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
2planet
planetgrav
R
mmGF
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)
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.
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
planetgrav
R
mmGF
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
mmGmg
This part is g
