A sphere of mass 3.75 grams is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of 32.9° with the vertical. Find the magnitude of the push from the breeze. Answer in Newtons.
I know that there are 2 forces acting on the string, gravity and the breeze, but do I need to use equations of motions or ??? Help is greatly appreciated!
To find the magnitude of the push from the breeze, we can break down the forces acting on the sphere and then use trigonometry to solve for the magnitude of the push.
Let's consider the forces acting on the sphere:
1. The weight of the sphere, which acts vertically downward with a force equal to the mass of the sphere multiplied by the acceleration due to gravity (9.8 m/s²).
2. The push from the breeze, which acts horizontally and makes an angle of 32.9° with the vertical.
To find the magnitude of the push from the breeze, we can use trigonometry to determine the horizontal component of the weight force. This component will be balanced by the horizontal push from the breeze.
First, we need to find the vertical component of the weight force. Using trigonometry, we can calculate:
Vertical component of weight = Weight of the sphere * sin(angle)
Vertical component of weight = (3.75 grams * 9.8 m/s²) * sin(32.9°)
Next, we can calculate the horizontal component of the weight force:
Horizontal component of weight = Weight of the sphere * cos(angle)
Horizontal component of weight = (3.75 grams * 9.8 m/s²) * cos(32.9°)
To find the magnitude of the push from the breeze, we can equate it to the horizontal component of the weight force:
Magnitude of push from breeze = Horizontal component of weight
Now, we can convert the mass of the sphere to kilograms to get the force in Newtons:
Magnitude of push from breeze = (3.75 grams * 9.8 m/s²) * cos(32.9°) in Newtons
Solving this equation will give you the magnitude of the push from the breeze in Newtons.
tension T
force F horizontal
vertical: T cos 32.9 = m g
horizontal: T sin 32.9 = F