A sphere of mass 2.7 x 10^-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of 41 degrees with the vertical. Find the magnitude of the push provided by the breeze and Find the tension in the cord.
you have a downward force of mg, and a horizontal force of F.
Tan theta=F/mg
solve for F.
Is that how to find the magnitude of the force of the breeze or the force of the Tension? I have to find two forces. thanks.
consider what the sine of the angle equals.
To find the magnitude of the push provided by the breeze, you need to consider the component of the gravitational force that is perpendicular to the cord. This is given by mg sin(θ), where θ is the angle the cord makes with the vertical.
Thus, the magnitude of the push provided by the breeze is equal to mg sin(θ).
To find the tension in the cord, you can consider the component of the gravitational force that is parallel to the cord. This is given by mg cos(θ).
Let's calculate both values using the given information:
Given:
Mass of the sphere, m = 2.7 x 10^-4 kg
Angle of the cord with the vertical, θ = 41 degrees
Gravitational force, Fg = mg
Magnitude of the push provided by the breeze, F = mg sin(θ)
F = (2.7 x 10^-4 kg)(9.8 m/s^2) sin(41 degrees)
F ≈ 0.00159 N
Tension in the cord, T = mg cos(θ)
T = (2.7 x 10^-4 kg)(9.8 m/s^2) cos(41 degrees)
T ≈ 0.00207 N
Therefore, the magnitude of the push provided by the breeze is approximately 0.00159 N, and the tension in the cord is approximately 0.00207 N.