A sphere of mass 3.3 10-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes an angle of 41° with the vertical when at rest

(a) Find the magnitude of that push.
(b) Find the tension in the cord.

Use the triangle.

tan41=horizonal push/mg

Then,
cos41=mg/tension

To find the magnitude of the push and the tension in the cord, you'll need to use a combination of trigonometry and force analysis.

Let's start with the magnitude of the push.

(a) Finding the magnitude of the push:
In this scenario, the force of the breeze causing the sphere to move sideways can be resolved into two components: one vertical and one horizontal. The vertical component of the force has no effect on the angle the cord makes with the vertical. Therefore, we only need to consider the horizontal component of the force.

The horizontal component of the push is equal to the tension in the cord, as it is the force that counteracts the tension and keeps the sphere in equilibrium.

Using trigonometry, we can find the horizontal component of the force:
Horizontal Component of Force = Tension * cos(angle)

where:
Tension is the tension in the cord
Angle is the angle the cord makes with the vertical (41° in this case)

Now we can set up the equation:

Tension * cos(41°) = Horizontal Component of Force

We need to isolate the tension, so divide both sides of the equation by cos(41°):

Tension = Horizontal Component of Force / cos(41°)

(b) Finding the tension in the cord:
To find the tension in the cord, we need to use Newton's second law, which states:

Sum of Forces = Mass * Acceleration

In this scenario, the only force acting on the sphere is the tension in the cord. Since the sphere is at rest, the acceleration is zero. Therefore, the sum of forces must also be zero.

Sum of Forces = Tension - mg = 0

where:
m is the mass of the sphere
g is the acceleration due to gravity (approximately 9.8 m/s^2)

Rearrange the equation to solve for the tension:

Tension = mg

Substitute the value of m into the equation:

Tension = (3.3 * 10^-4 kg) * (9.8 m/s^2)

Now you have the tension in the cord.

So, to summarize:

(a) The magnitude of the push is given by:
Magnitude of Push = Horizontal Component of Force = Tension * cos(angle)

(b) The tension in the cord is given by:
Tension = (3.3 * 10^-4 kg) * (9.8 m/s^2)