Newton's Law Question Involving Tow Truck

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Homework Statement

A tow truck pulls on a stuck car with a force of 3000N. The tow cable is under tension and pulls downward and to the left on the pin at its upper end. The pin is held in equilibrium by forces exerted by 2 bars A and B which are connected to the pin.

The diagram shows that the tow cable is at 60 degrees to the vertical, strut A is vertical and strut B is at 50 degrees to the horizontal. ( I hope this is clear)

Determine the force on each strut and whether it is of tension or compression.

Homework Equations

Newton's Laws

The Attempt at a Solution

I didn't take the forces (normal, friction and weight) of the car into account because I didn't think they were relevant to this question and I don't think I have enough given numerical values anyway...
Having drawn a free body diagram, I determined that the force on A was of tension and force on B was of compression.
Tc = tension of cable = 3000N
Ta = tension of strut A
Tb =compression force of strut B

Hence:
sigma(Fx)=Tcsin60 +Tbcos50 = 0
which gives Tb = 947.631...N = 950N
sigma(Fy)=Tccos60 +Ta +Tbsin50=0
substituting Tb gives Ta = 2608.604...N =2700N

But the answers are wrong. I think that at least the sum of my forces in the x direction are incorrect...but I don't know what to do because all i have is the applied force and angles...

 

[anathema]

Thank you for your post. Your approach to the problem is correct, but there are a few small errors in your calculations.

Firstly, your equation for the x-direction should be:

ΣFx = Tcsin60 - Tbcos50 = 0

This is because the force from the cable is pulling to the left (negative direction) and the force from strut B is pushing to the right (positive direction).

Next, when you substitute for Tb, you should get Ta = 2603.641...N = 2600N, not 2608.604...N. This is because you have rounded Tb to 950N, but you have used the full value for Tb in your calculation (947.631...N).

Using these corrected values, your final answer should be:

Ta = 2600N (tension)
Tb = 950N (compression)

I hope this helps. Keep up the good work in your scientific studies!

 

[nlightner]

As a scientist, it is important to always consider all relevant forces and factors in a given situation, even if they may not seem immediately relevant. In this case, the weight and friction of the car may not be explicitly given, but they do play a role in the equilibrium of the pin and should be taken into account in order to accurately determine the forces on the struts.

It is also important to carefully consider the angles and directions of the forces being applied. In this case, the angle of the tow cable and the angles of the struts are crucial in determining the correct forces.

Additionally, it may be helpful to use trigonometric functions to accurately calculate the forces on the struts, rather than simply using the given angles and forces. This will help to ensure that all forces are accounted for and the correct values are obtained.

In conclusion, as a scientist it is important to carefully consider all relevant factors and use appropriate calculations and techniques in order to accurately solve problems and determine solutions.