Solving 2 Physics Questions | 65 Characters

[lotusbloom]

2 physics Questions...

1. There is a clever kitchen gadget for drying lettuce leaves after you wash them. It consists of a cylindrical container mounted so that it can be rotated about its axis by turning a hand crank. The outer wall of the cylinder is perforated with small holes. You put the wet leaves in the container and turn the crank to spin off the water. The radius of the container is 10.2 cm. When the cylinder is rotating at 2.61 revolutions per second, what is the magnitude of the centripetal acceleration at the outer wall?

2.A car is safely negotiating an unbanked circular turn at a speed of 19.2 m/s. The maximum static frictional force acts on the tires. Suddenly a wet patch in the road reduces the maximum static frictional force by a factor of three. If the car is to continue safely around the curve, to what speed must the driver slow the car?

please help..thanks...

 

[Chen]

1. Let's get rid of all the excess information (dear God, there is a lot of it!) - we know that the raduis is 0.102 meters and the frequency of the motion is 2.61Hz. Is this enough to find the centripetal acceleration? Let's see. You should know that a_c = v²/r. But since v = ωr we can say that a_c = ω²r. We have r, so we just need to find ω now... can you do it yourself?

 

[Chen]

2. For the car "to continue safely around the curve", the static frictional force must match the centripetal force that the car should experience as it goes around the curve. So:

$$f_{s_{max}} = F_c$$

Let's expand it a bit:

$$mg\mu _s = ma_c = m\frac{v^2}{r}$$

As the mass cancels we are left with:

$$gr\mu _s = v^2$$

So if $\mu _s$ is reduced by a factor of three, what must be the new speed of the car?

 

[lotusbloom]

1. Let's get rid of all the excess information (dear God, there is a lot of it!) - we know that the raduis is 0.102 meters and the frequency of the motion is 2.61Hz. Is this enough to find the centripetal acceleration? Let's see. You should know that a_c = v²/r. But since v = ωr we can say that a_c = ω²r. We have r, so we just need to find ω now... can you do it yourself?

so a_c = ω²r to find W...is a_c = 2.61Hz and r =0.102m put it into find W then put w in v=wr equation to find V?

 

[lotusbloom]

2. For the car "to continue safely around the curve", the static frictional force must match the centripetal force that the car should experience as it goes around the curve. So:

$$f_{s_{max}} = F_c$$

Let's expand it a bit:

$$mg\mu _s = ma_c = m\frac{v^2}{r}$$

As the mass cancels we are left with:

$$gr\mu _s = v^2$$

So if $\mu _s$ is reduced by a factor of three, what must be the new speed of the car?

So the new speed will reduces by three too..is that right?

 

[Chen]

so a_c = ω²r to find W...is a_c = 2.61Hz and r =0.102m put it into find W then put w in v=wr equation to find V?

No, it is the frequency, f = 2.61Hz. You still don't know a_c, you need to find it. ω is the angular velocity, right? So if the cylinder is rotating at 2.61 revolutions per second, how many radians does it rotate by every second? (Hint: Every circle has 2π radians.)

 

[Chen]

So the new speed will reduces by three too..is that right?

No.

$$gr\mu _s = v^2$$

If $gr\mu _s$ is reduced by a factor of 3, how much is v² reduced by? How much is v reduced by then?

 

[lotusbloom]

No, it is the frequency, f = 2.61Hz. You still don't know a_c, you need to find it. ω is the angular velocity, right? So if the cylinder is rotating at 2.61 revolutions per second, how many radians does it rotate by every second? (Hint: Every circle has 2π radians.)

ok i think it got it...so w=5.22, r=10.2cm ( do i need to change that into m)...so then i can find a_c right? then using a_c = v^2/r...i can find the velocity right?

 

[lotusbloom]

No.

$$gr\mu _s = v^2$$

If $gr\mu _s$ is reduced by a factor of 3, how much is v² reduced by? How much is v reduced by then?

ok for this one i got an answer of 10.2 m/s...but is wrong...and i don't know why...

 

[Chen]

ok i think it got it...so w=5.22, r=10.2cm ( do i need to change that into m)...so then i can find a_c right? then using a_c = v^2/r...i can find the velocity right?

No, ω = 5.22π = 16.4 rad/s. And yes, you need to convert r to meters to get the units of the acceleration correct.

 

[Chen]

ok for this one i got an answer of 10.2 m/s...but is wrong...and i don't know why...

How can you get a value for v? The question asked to find how much it would be reduced by if the coefficient of friction was reduced by a factor of 3. If you reduce the value of x² by a factor of 3, how much is x itself reduced by?