Find Tension & Force of Air Current for Suspended Wooden Ball

[angi-18]

my question is:
a wooden ball of mass 100gm is suspended by a string.The horizontal current of air blows it to one side such that the thread makes an angle of 30° with the vertical find the tension in the thread and the force of air current.

i have used this formula: T=mg but it does not work as the angle is also given...:uhh:

and the answers are : 1.131N and 0.565N
m not getting the correct answer even...:(

 

[cepheid]

my question is:
a wooden ball of mass 100gm is suspended by a string.The horizontal current of air blows it to one side such that the thread makes an angle of 30° with the vertical find the tension in the thread and the force of air current.

i have used this formula: T=mg but it does not work as the angle is also given...:uhh:

and the answers are : 1.131N and 0.565N
m not getting the correct answer even...:(

T = mg only works if the string is vertical and no other forces are acting except gravity. That's not true here.

Draw a free body diagram for the ball, including all of the forces acting on it. Then use Newton's 2nd law and the fact that the ball is not moving to solve for the forces. Hint: the ball is not moving. What does this mean about the sum of all forces acting on it?

 

[angi-18]

what would be the formula as the θ is given ?

 

[cepheid]

what would be the formula as the θ is given ?

You get to figure out the equation yourself. Did you draw a diagram of all of the forces? Hint: it is easiest to consider Newton's second law separately for horizontal and vertical forces. To do this, you'll need to resolve the tension force into x and y components (which is where θ comes in).

 

[angi-18]

ok let me try..

 

[angi-18]

force of gravity is acting on it and force of air (which we have to find)

 

[angi-18]

F=ma
and
Fx=Fsin30
Fy=Fcos 30

we have to do like this ??

 

[cepheid]

force of gravity is acting on it and force of air (which we have to find)

Don't forget the tension!

F=ma

Yes, the "F" here is the NET force (i.e. the total force acting, once you have summed up all of the individual ones). In this case it must be 0, because a = 0.

and
Fx=Fsin30
Fy=Fcos 30

we have to do like this ??

Yes, this is how you would resolve the tension into x and y components. Now, to proceed, write down two equations:

sum of forces in horizontal direction = 0
sum of forces in vertical direction = 0

These two equations should allow you to solve for all the unknown forces.