How Do I Find the Angle of Force in This Scenario?

[homevolend]

Homework Statement

Question in angle of force: A women is pulling a rock attached to a rope with 10N of force. If the mass of the rope&rock is 30 kg. And if the rope&rock accelerate at 5 m/s squared without friction. What is the angle to the horizonal ground does the woman pull?

Homework Equations

Mass= 30kg
Fnet=10N
A=5m/s^2

The Attempt at a Solution

What I tried to do was use this forumula: (m)(a)=(Fnet)Cos(theta)-Ff

So then I tried to do the 30*5 which is 150 = 10cos-1 But I could find the angle.

I do not know how to corrently find the angle in these types of questions.




thanks!

 

[Delphi51]

150 = 10cos(θ)
15 = cos(θ)
but there is no solution. This is because you need more than 10 N to accelerate 30 kg at 5 m/s². In fact, you need 150 N when pulling straight ahead. Is it possible you have copied a number in the question incorrectly?

 

[homevolend]

Yes sorry I did, it is f40N, m=10kg, a=3.5ms/s/s

I was looking at a different quesion. I just cannot seem to find a way to find the angle. I tried drawing a diagram to no avail.

 

[Delphi51]

F=ma
40*cos(Θ) = 10*3.5
cos(Θ) = 35/40
cos(Θ) = 0.875
Now take the inverse cosine of both sides to get
Θ = invCos(0.875)
Θ = 29 degrees

 

[homevolend]

Thanks! Now I will know how to find the Θ for my next questions like this. Thanks again, appreciate it.

 

[Delphi51]

Most welcome!