- #1
Thickmax
- 31
- 8
- Homework Statement
- Engineering course top up physics module
- Relevant Equations
- See below
I've checked my answer many times and do not understand what I am missing
Thickmax said:answer is apparently
1/(M*g*v)*(P-C*v^3) No idea how this is the case
Thanks Very much!Delta2 said:The crane is moving with constant horizontal velocity. Hence the vector sum of the horizontal forces is zero, that is
$$\vec{F}_{resistance}+\vec{F}_{driving}=\vec{0}$$
In order to transform the above vector equation to an algebraic equation , you have to be careful with signs and conventions. If we make the convention that the positive direction is towards right , then $$\vec{F}_{driving}=\frac{P}{v}\hat x$$ that is it is positive force, but $$\vec{F}_{resistance}=-Cv^2\hat x-\mu mg\hat x$$, that is it is negative (towards the left).
Thus the initial vector equation will transform to the algebraic equation
$$-Cv^2-\mu mg+\frac{P}{v}=0$$ which you can solve for ##\mu## and you will get what you saying at post #3.
Thickmax said:Am I missing something?
How do you know when to do that? Is this method called something that i can read up on?Delta2 said:No you got it right, you just need one last algebraic step: multiply both the numerator and the denominator of the fraction by v and then you 'll get what you say at post #3.
Ehm its fundamental algebraic rule: IF you multiply both the numerator and the denominator of a fraction with the same thing, the fraction remains the same. That is $$\frac{a}{b}=\frac{ac}{bc}$$Thickmax said:How do you know when to do that? Is this method called something that i can read up on?
Oh I see nowBut how do you know when to do that? Is it just to tidy up the equation and have ‘one line’ as the numerator?Delta2 said:Ehm its fundamental algebraic rule: IF you multiply both the numerator and the denominator of a fraction with the same thing, the fraction remains the same. That is $$\frac{a}{b}=\frac{ac}{bc}$$
Yes you can view it like this.Thickmax said:Oh I see nowBut how do you know when to do that? Is it just to tidy up the equation and have ‘one line’ as the numerator?
Yes, it is usual to avoid nested fractions in the simplified form. But more generally, you cannot assume the target form is what you would consider the simplest such. You have to be prepared to check whether there is some way of manipulating the one into the other.Thickmax said:Oh I see nowBut how do you know when to do that? Is it just to tidy up the equation and have ‘one line’ as the numerator?
A force is a push or pull that can cause an object to accelerate or change its motion.
The different types of forces acting on a moving crane include:
The forces acting on a moving crane can affect its stability in different ways. For example, if the force of gravity is greater than the tension in the crane's cables, it can cause the crane to tip over. Friction can also play a role in stability, as it can either help to keep the crane in place or make it more difficult to move. Properly balancing and controlling these forces is crucial for maintaining the stability of a moving crane.
When operating a crane, it is important to follow all safety protocols and guidelines. This includes ensuring that the crane is properly maintained and inspected, using the correct equipment and techniques for the job, and following proper load limits and weight distribution. It is also important to have a trained and experienced operator in control of the crane at all times.
The forces acting on a moving crane can be calculated using mathematical formulas and principles of physics. This information can then be used to determine the necessary counterweights, tension in cables, and other factors to maintain the stability and control of the crane. Additionally, advanced technologies such as sensors and computer systems can help monitor and regulate these forces in real-time to ensure safe and efficient operation of the crane.