How Do You Calculate Cosine Theta from Work, Force, and Distance?

[Lord Amirul]

Homework Statement

In the diagram , a block rests on a smooth horizontal surface . It is then pushed with a force of 45 N at an angle of Θ(theta) to the horizontal . 50 J of work has been done to push the block through a distance of 1.60 m Its speed is 2.50 m s^-1.

Homework Equations

The Attempt at a Solution

I know how to find joule . but this time , it is given joule and to find the angle
the formula I use for finding joule is W = F x d x costine(theta)
however , this time it is like costine(theta) = W x F x d

 

[Let'sthink]

The last step in your calculation got muddled up
cos theta = 50/(45*1.60) = 0.6944 or theta = 46°

 

[Let'sthink]

The problem is over defined, you can find the mass of the block as its velocity at the end of 1.60 m travel is given how think?

 

[haruspex]

however , this time it is like costine(theta) = W x F x d

No, it's still W cos(theta) = F x d. It's just that you know W, F and d and wish to find theta.

The problem is over defined, you can find the mass of the block as its velocity at the end of 1.60 m travel is given how think?

It is not over-defined. If it were, you would be able to derive some of the given information from other given information. There is redundant information.

 

[Let'sthink]

m = [(2*50)/{2.50²}] = 16 kg
a = [(2.50²)/(2*1.60)] = 1.953125
Fx = 16*1.953125 = 31.25 N
cos theta = 31.25/45 = 0.6944 or theta = 46°
I have not used the work done formula.
May be that is what you mean by redundant for work done.

 

[haruspex]

m = [(2*50)/{2.50²}] = 16 kg
a = [(2.50²)/(2*1.60)] = 1.953125
Fx = 16*1.953125 = 31.25 N
cos theta = 31.25/45 = 0.6944 or theta = 46°
I have not used the work done formula.
May be that is what you mean by redundant for work done.

It's not a question of which formulae you use, but of which information you use.
Suppose you had not been told the final velocity. You could not then determine the mass, but you could still go through the sequence you posted above using unknowns for those and arrive at the answer. In effect, you will have used the work done formula, but disguised as a sequence of other formulae from which it can be deduced.

Redundant information is merely information that is of no help in finding the answer. Since the mass here is not given, the final velocity falls into that category. You could change the final velocity to any number you like, keeping all other given information the same. The mass will change, but the work done will not.

A problem is overspecified if you can use different minimal subsets of the given information to arrive at the answer. In this case, some of the given information can be deduced from other given information. In some cases, they may even be in conflict, with the result that you will get different answers to the question according to which way you solve it. (This does happen!)

 

[Let'sthink]

I agree with you haruspex, I should have used the term redundant in place of over defined for which now you have given the right term over specified. I am sorry for my terminological in-exactitude.

 

[Lord Amirul]

thank you so much . All of your answers help me a lot .