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To do a problem like this, we find the acceleration required (in

variables) and use this to find required a force. This force comes fromfriction.

The force required is...

This force comes from friction

Solving this for time gives us the required time for various coefficientsof friction.

Problem 1Saturday, May 19, 2012

9:03 AM

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Because we don't yet know the coefficient of friction in this step, we

have to use kinematics to solve this.

Plugging (1) into (2)


9:03 AM

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The magnitude of the frictional force is the coefficient of friction times

the normal force.

Because the velocity is down the ramp, the frictional force is applied up

the ramp.

This is another kinematics problem. We know the acceleration and the

distance so...

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Problem 3Wednesday, May 16, 2012

11:23 PM

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Plugging this back into the blue x-equation.

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For this problem, we have a free-body diagram that looks like...

As we can see here, the friction force is what keeps the eggs moving on

a circular path. The two equations that this gives us are...

Plugging Eq (1) into Eq (2), we can solve for velocity.


9:04 AM

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Need the free-body diagram...

From this diagram, I get the equation

Solving this for velocity

The force exerted by the seat is the force provided by the ropes. Both

of the ropes contribute a force ofT. That means the force provided by

the seat is 2T.


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Here we have Indiana Jones at the bottom of his swing. The free-body

diagram looks like...

From this, we get the equation...

We can solve this to find the tension in the rope at the bottom of the

arc.

If the rope can only support 1,000 N, then the rope is going to break.


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For a lot of this, it will be helpful to have our free-body diagram.

By using a coordinate system like,this, we have radial acceleration in

the y-problem and tangential

acceleration in the x-problem.

We have two equations...


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Tension in the string can be found from the first equation.

The radial component of acceleration is

The tangential equation is where we find the tangential acceleration.

The total acceleration is the vector sum of these two.

The angle that this acceleration makes with the cable (shown above)

can by found by using the tangent.

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The answer does not change if the swing is down instead of up. This is

because everywhere we have a velocity, it is squared. We loose the

direction info and everything is the same.

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This is taking place in an accelerated reference frame. We have a

fictitious force that is causing this angular displacement (assuming we

are standing on the truck). If we are outside the truck, this angular

displacement happens because there is an acceleration. Let's look at

the free-body diagram.

We get two equations from this diagram.

To find the angle, we can solve the first equation for Tand plug it into


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We can make the free-body diagrams of each of these masses.

We already have enough information to find T1.

We can use this value ofT1 in the other equation to find T2.


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In this situation, I can already tell that T2 is always going to have a

higher tension than T1. That means string 2 is more likely to break first.

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