How to calculate coefficient of static friction given certain data
I'm trying to work out a question where I need to calculate the coefficient of friction given the radius of the corner, the angle of the bank and the speed at which the corner can be taken.
Specifically the question says
A speedway has banked turns of 31° and a radius of 304.8 m. Drivers can go through the corners at a speed of 322 km/h before slipping. What is the coefficient of friction between the tires and the road?
Is there a generic formula that I could use? If not could I get some help working this out? Thanks in advance.
physics classical-mechanics
edited Mar 23 '17 at 20:40
Jean Marie
28.7k41849
asked Mar 23 '17 at 18:43
Ian Faurschou
62
add a comment |
I'm trying to work out a question where I need to calculate the coefficient of friction given the radius of the corner, the angle of the bank and the speed at which the corner can be taken.
Specifically the question says
A speedway has banked turns of 31° and a radius of 304.8 m. Drivers can go through the corners at a speed of 322 km/h before slipping. What is the coefficient of friction between the tires and the road?
Is there a generic formula that I could use? If not could I get some help working this out? Thanks in advance.
physics classical-mechanics
edited Mar 23 '17 at 20:40
Jean Marie
28.7k41849
asked Mar 23 '17 at 18:43
Ian Faurschou
62
This is a question about physics, not about mathematics and is better suited to physics stack exchange
– Stella Biderman
Mar 23 '17 at 18:44
best delete this question after reposting it
– Stella Biderman
Mar 23 '17 at 18:49
3
It's a valid question in the Classical Mechanics category, so there's no need to delete it. Do you want an answer?
– David Quinn
Mar 23 '17 at 18:52
I think in physics.SE they'll not answer this question. Questions in Physics.SE that belong to homework should ask to specific concepts in the physics of the problem and not how the math o the problem should be used. Usually.
– Rafael Wagner
Mar 23 '17 at 18:53
add a comment |
I'm trying to work out a question where I need to calculate the coefficient of friction given the radius of the corner, the angle of the bank and the speed at which the corner can be taken.
Specifically the question says
A speedway has banked turns of 31° and a radius of 304.8 m. Drivers can go through the corners at a speed of 322 km/h before slipping. What is the coefficient of friction between the tires and the road?
Is there a generic formula that I could use? If not could I get some help working this out? Thanks in advance.
physics classical-mechanics
edited Mar 23 '17 at 20:40
Jean Marie
28.7k41849
asked Mar 23 '17 at 18:43
Ian Faurschou
62
I'm trying to work out a question where I need to calculate the coefficient of friction given the radius of the corner, the angle of the bank and the speed at which the corner can be taken.
Specifically the question says
A speedway has banked turns of 31° and a radius of 304.8 m. Drivers can go through the corners at a speed of 322 km/h before slipping. What is the coefficient of friction between the tires and the road?
Is there a generic formula that I could use? If not could I get some help working this out? Thanks in advance.
physics classical-mechanics
physics classical-mechanics
edited Mar 23 '17 at 20:40
Jean Marie
28.7k41849
asked Mar 23 '17 at 18:43
Ian Faurschou
62
edited Mar 23 '17 at 20:40
Jean Marie
28.7k41849
asked Mar 23 '17 at 18:43
Ian Faurschou
62
edited Mar 23 '17 at 20:40
Jean Marie
28.7k41849
edited Mar 23 '17 at 20:40
Jean Marie
28.7k41849
edited Mar 23 '17 at 20:40
Jean Marie
28.7k41849
28.7k41849
asked Mar 23 '17 at 18:43
Ian Faurschou
62
asked Mar 23 '17 at 18:43
Ian Faurschou
62
asked Mar 23 '17 at 18:43
Ian Faurschou
62
62
This is a question about physics, not about mathematics and is better suited to physics stack exchange
– Stella Biderman
Mar 23 '17 at 18:44
best delete this question after reposting it
– Stella Biderman
Mar 23 '17 at 18:49
3
It's a valid question in the Classical Mechanics category, so there's no need to delete it. Do you want an answer?
– David Quinn
Mar 23 '17 at 18:52
I think in physics.SE they'll not answer this question. Questions in Physics.SE that belong to homework should ask to specific concepts in the physics of the problem and not how the math o the problem should be used. Usually.
– Rafael Wagner
Mar 23 '17 at 18:53
add a comment |
This is a question about physics, not about mathematics and is better suited to physics stack exchange
– Stella Biderman
Mar 23 '17 at 18:44
best delete this question after reposting it
– Stella Biderman
Mar 23 '17 at 18:49
3
It's a valid question in the Classical Mechanics category, so there's no need to delete it. Do you want an answer?
– David Quinn
Mar 23 '17 at 18:52
I think in physics.SE they'll not answer this question. Questions in Physics.SE that belong to homework should ask to specific concepts in the physics of the problem and not how the math o the problem should be used. Usually.
– Rafael Wagner
Mar 23 '17 at 18:53
This is a question about physics, not about mathematics and is better suited to physics stack exchange
– Stella Biderman
Mar 23 '17 at 18:44
This is a question about physics, not about mathematics and is better suited to physics stack exchange
– Stella Biderman
Mar 23 '17 at 18:44
best delete this question after reposting it
– Stella Biderman
Mar 23 '17 at 18:49
best delete this question after reposting it
– Stella Biderman
Mar 23 '17 at 18:49
3
3
It's a valid question in the Classical Mechanics category, so there's no need to delete it. Do you want an answer?
– David Quinn
Mar 23 '17 at 18:52
It's a valid question in the Classical Mechanics category, so there's no need to delete it. Do you want an answer?
– David Quinn
Mar 23 '17 at 18:52
I think in physics.SE they'll not answer this question. Questions in Physics.SE that belong to homework should ask to specific concepts in the physics of the problem and not how the math o the problem should be used. Usually.
– Rafael Wagner
Mar 23 '17 at 18:53
I think in physics.SE they'll not answer this question. Questions in Physics.SE that belong to homework should ask to specific concepts in the physics of the problem and not how the math o the problem should be used. Usually.
– Rafael Wagner
Mar 23 '17 at 18:53
add a comment |
1 Answer
1
active
oldest
votes
The problem of a banked turn with friction is worked out on Wikipedia, where the following equation for maximal velocity is derived:
$$
v= {sqrt{rgleft(sin theta +mu_s cos theta right)over cos theta -mu_s sin theta }}
={sqrt{rgleft(tantheta +mu_sright)over 1 -mu_s tantheta}}.
$$
This equation expresses the maximum velocity $v$ in terms of the angle of incline $theta$, coefficient $mu_s$ of static friction, and radius $r$ of curvature; $gapprox9.8,{rm m}/{rm s}^2$.
Squaring both sides of the equation and isolating $mu_s$ we find
$$
mu_s = {v^2-rgtanthetaover v^2tantheta+rg}.
$$
Now it remains to substitute the given values:
$$
theta=31^circ, quad
v=322,{rm km}/{rm h}approx 89.44,{rm m}/{rm s}, quad
r=304.8,{rm m}, quad
gapprox9.8,{rm m}/{rm s}^2.
$$
Substitution yields
$$
mu_s approx 0.796
$$
answered Mar 23 '17 at 19:50
Alex
4,2151628
Note that this is not static friction, is the kinetic friction coefficient
– Rafael Wagner
Mar 23 '17 at 19:51
1
The words "before slipping" in the problem statement mean that the wheels do not slip up the incline, so $mu_s$ applies to our case.
– Alex
Mar 23 '17 at 19:54
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
The problem of a banked turn with friction is worked out on Wikipedia, where the following equation for maximal velocity is derived:
$$
v= {sqrt{rgleft(sin theta +mu_s cos theta right)over cos theta -mu_s sin theta }}
={sqrt{rgleft(tantheta +mu_sright)over 1 -mu_s tantheta}}.
$$
This equation expresses the maximum velocity $v$ in terms of the angle of incline $theta$, coefficient $mu_s$ of static friction, and radius $r$ of curvature; $gapprox9.8,{rm m}/{rm s}^2$.
Squaring both sides of the equation and isolating $mu_s$ we find
$$
mu_s = {v^2-rgtanthetaover v^2tantheta+rg}.
$$
Now it remains to substitute the given values:
$$
theta=31^circ, quad
v=322,{rm km}/{rm h}approx 89.44,{rm m}/{rm s}, quad
r=304.8,{rm m}, quad
gapprox9.8,{rm m}/{rm s}^2.
$$
Substitution yields
$$
mu_s approx 0.796
$$
answered Mar 23 '17 at 19:50
Alex
4,2151628
Note that this is not static friction, is the kinetic friction coefficient
– Rafael Wagner
Mar 23 '17 at 19:51
1
The words "before slipping" in the problem statement mean that the wheels do not slip up the incline, so $mu_s$ applies to our case.
– Alex
Mar 23 '17 at 19:54
add a comment |
The problem of a banked turn with friction is worked out on Wikipedia, where the following equation for maximal velocity is derived:
$$
v= {sqrt{rgleft(sin theta +mu_s cos theta right)over cos theta -mu_s sin theta }}
={sqrt{rgleft(tantheta +mu_sright)over 1 -mu_s tantheta}}.
$$
This equation expresses the maximum velocity $v$ in terms of the angle of incline $theta$, coefficient $mu_s$ of static friction, and radius $r$ of curvature; $gapprox9.8,{rm m}/{rm s}^2$.
Squaring both sides of the equation and isolating $mu_s$ we find
$$
mu_s = {v^2-rgtanthetaover v^2tantheta+rg}.
$$
Now it remains to substitute the given values:
$$
theta=31^circ, quad
v=322,{rm km}/{rm h}approx 89.44,{rm m}/{rm s}, quad
r=304.8,{rm m}, quad
gapprox9.8,{rm m}/{rm s}^2.
$$
Substitution yields
$$
mu_s approx 0.796
$$
answered Mar 23 '17 at 19:50
Alex
4,2151628
Note that this is not static friction, is the kinetic friction coefficient
– Rafael Wagner
Mar 23 '17 at 19:51
1
The words "before slipping" in the problem statement mean that the wheels do not slip up the incline, so $mu_s$ applies to our case.
– Alex
Mar 23 '17 at 19:54
add a comment |
The problem of a banked turn with friction is worked out on Wikipedia, where the following equation for maximal velocity is derived:
$$
v= {sqrt{rgleft(sin theta +mu_s cos theta right)over cos theta -mu_s sin theta }}
={sqrt{rgleft(tantheta +mu_sright)over 1 -mu_s tantheta}}.
$$
This equation expresses the maximum velocity $v$ in terms of the angle of incline $theta$, coefficient $mu_s$ of static friction, and radius $r$ of curvature; $gapprox9.8,{rm m}/{rm s}^2$.
Squaring both sides of the equation and isolating $mu_s$ we find
$$
mu_s = {v^2-rgtanthetaover v^2tantheta+rg}.
$$
Now it remains to substitute the given values:
$$
theta=31^circ, quad
v=322,{rm km}/{rm h}approx 89.44,{rm m}/{rm s}, quad
r=304.8,{rm m}, quad
gapprox9.8,{rm m}/{rm s}^2.
$$
Substitution yields
$$
mu_s approx 0.796
$$
answered Mar 23 '17 at 19:50
Alex
4,2151628
The problem of a banked turn with friction is worked out on Wikipedia, where the following equation for maximal velocity is derived:
$$
v= {sqrt{rgleft(sin theta +mu_s cos theta right)over cos theta -mu_s sin theta }}
={sqrt{rgleft(tantheta +mu_sright)over 1 -mu_s tantheta}}.
$$
This equation expresses the maximum velocity $v$ in terms of the angle of incline $theta$, coefficient $mu_s$ of static friction, and radius $r$ of curvature; $gapprox9.8,{rm m}/{rm s}^2$.
Squaring both sides of the equation and isolating $mu_s$ we find
$$
mu_s = {v^2-rgtanthetaover v^2tantheta+rg}.
$$
Now it remains to substitute the given values:
$$
theta=31^circ, quad
v=322,{rm km}/{rm h}approx 89.44,{rm m}/{rm s}, quad
r=304.8,{rm m}, quad
gapprox9.8,{rm m}/{rm s}^2.
$$
Substitution yields
$$
mu_s approx 0.796
$$
answered Mar 23 '17 at 19:50
Alex
4,2151628
edited Apr 5 '17 at 1:46
answered Mar 23 '17 at 19:50
Alex
4,2151628
answered Mar 23 '17 at 19:50
Alex
4,2151628
answered Mar 23 '17 at 19:50
Alex
4,2151628
4,2151628
Note that this is not static friction, is the kinetic friction coefficient
– Rafael Wagner
Mar 23 '17 at 19:51
1
The words "before slipping" in the problem statement mean that the wheels do not slip up the incline, so $mu_s$ applies to our case.
– Alex
Mar 23 '17 at 19:54
add a comment |
Note that this is not static friction, is the kinetic friction coefficient
– Rafael Wagner
Mar 23 '17 at 19:51
1
The words "before slipping" in the problem statement mean that the wheels do not slip up the incline, so $mu_s$ applies to our case.
– Alex
Mar 23 '17 at 19:54
Note that this is not static friction, is the kinetic friction coefficient
– Rafael Wagner
Mar 23 '17 at 19:51
Note that this is not static friction, is the kinetic friction coefficient
– Rafael Wagner
Mar 23 '17 at 19:51
1
1
The words "before slipping" in the problem statement mean that the wheels do not slip up the incline, so $mu_s$ applies to our case.
– Alex
Mar 23 '17 at 19:54
The words "before slipping" in the problem statement mean that the wheels do not slip up the incline, so $mu_s$ applies to our case.
– Alex
Mar 23 '17 at 19:54
add a comment |
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This is a question about physics, not about mathematics and is better suited to physics stack exchange
– Stella Biderman
Mar 23 '17 at 18:44
best delete this question after reposting it
– Stella Biderman
Mar 23 '17 at 18:49
3
It's a valid question in the Classical Mechanics category, so there's no need to delete it. Do you want an answer?
– David Quinn
Mar 23 '17 at 18:52
I think in physics.SE they'll not answer this question. Questions in Physics.SE that belong to homework should ask to specific concepts in the physics of the problem and not how the math o the problem should be used. Usually.
– Rafael Wagner
Mar 23 '17 at 18:53