# How can I solve problem 2/120 without knowing the vectors for the cross product?

• charlies1902
In summary, the student is having trouble solving for Mz in a problem that is most easily solved if you express each vector in unit vector notation. He is unclear on how to write vector r in unit vector notation. For vector P, he first needs to write it in terms of two unit vectors, one along the normal n and one along the z-axis. Once he has done this, he can write n in terms of unit vectors along the x and y axes. Finally, he needs to write r in terms of unit vector notation.
charlies1902

## Homework Statement

http://books.google.com/books?id=0g...m=1&sqi=2&ved=0CBgQ6AEwAA#v=onepage&q&f=false

problem 2/120 is the question I'm having a hard time with. I know how to do everything except I just can't EYE this one.

I would like to solve for Mz by taking the cross product rxF. but I don't know how to get those vectors for this problem.

This problem is most easily done if you express each vector in unit vector notation, then take the cross product.

Can you write vector r in unit vector notation?

For vector P you first need to write it in terms two unit vectors, one along the normal n and one along the z-axis. Once you have done this, write n in terms of unit vectors along the x and y axes and you're done.

kuruman said:
This problem is most easily done if you express each vector in unit vector notation, then take the cross product.

Can you write vector r in unit vector notation?

For vector P you first need to write it in terms two unit vectors, one along the normal n and one along the z-axis. Once you have done this, write n in terms of unit vectors along the x and y axes and you're done.

doesn't having them both in unit vector notation means you'll get a diff magntitude when taking the cross product than if you were to take the cross product without the unit vector?

Perhaps you don't understand unit vector notation. If vector A has components Ax= 3 units and Ay= 4 units, we would write it in unit vector notation as
$\vec{A}=3\widehat{x}+4\widehat{y}$ units,
where $\hat{x}$ stands for "in the x-direction" and $\hat{y}$ stands for "in the y-direction". So the above equation in plain English translates as "Vector A is the same as going three units in the x-direction and then going 4 units in the y-direction." Note that the magnitude of vector A is not one but five units. You get 5 by squaring whatever multiplies i-hat, adding to it the square of whatever multiplies j-hat and then taking the square root of this sum (Pythagorean theorem.)

pyroknife said:
doesn't having them both in unit vector notation means you'll get a diff magntitude when taking the cross product than if you were to take the cross product without the unit vector?

Of course not.

I'm confused now. I always thought unit vector notation was that the vector has a magnitude of 1. so for your vector wouldn't unit vector notation be 3/5i+4/5j??

pyroknife said:
I'm confused now. I always thought unit vector notation was that the vector has a magnitude of 1. so for your vector wouldn't unit vector notation be 3/5i+4/5j??
It would. I note that (3/5)i+(4/5)j is a unit vector (a vector of magnitude 1) that points along the direction of A. Observe that vector A, as I have written it in unit vector notation, is the magnitude of A times a unit vector in the direction of A, i.e. A=5[(3/5)i+(4/5)j] = 3i+4j units. In this problem, for r, you have to write down a vector that has magnitude 900 mm and looks like r = (so many mm)i+(so many other mm)j.

I got the right answer (208k) by shifting the x&y axis by 20 degrees thus making the force perpendicular with the y axis. Is that an accurate way to do it?

## 1. What is the difference between statics and dynamics?

Statics is the study of objects and systems in equilibrium, while dynamics is the study of objects and systems in motion. In other words, statics deals with objects at rest, while dynamics deals with objects in motion.

## 2. How do I calculate the net force on an object?

To calculate the net force on an object, you need to add up all the individual forces acting on the object. The net force is a vector quantity, meaning it has both magnitude and direction. It can be calculated by using the formula Fnet = ΣF, where ΣF represents the sum of all the forces.

## 3. What is the difference between mass and weight?

Mass is a measure of the amount of matter an object contains, while weight is a measure of the force of gravity on an object. Mass is usually measured in kilograms, while weight is measured in newtons. The mass of an object remains constant regardless of its location, while weight can change depending on the strength of gravity.

## 4. How do I determine the center of mass of an object?

The center of mass of an object is the point at which the object's mass is evenly distributed in all directions. To find the center of mass, you can use the formula xcm = (Σmixi)/(Σmi), where xi is the position of each individual mass and mi is the corresponding mass. This formula can be used for both one-dimensional and two-dimensional systems.

## 5. What is the difference between static and kinetic friction?

Static friction is the force that keeps an object at rest, while kinetic friction is the force that acts on an object in motion. Static friction is usually greater than kinetic friction, meaning it takes more force to overcome static friction and start an object moving than it takes to keep an object moving. Additionally, static friction acts in the opposite direction of the applied force, while kinetic friction acts in the direction of motion.

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