a 2kg ball revolves in a horizontal circle as shown at a constant speed of 1.5m/s. Knowing that L=600mm, determine (a) the angle that the cord with the vertical (b) tension in the cord.

a 2kg ball revolves in a horizontal circle as shown at a constant speed of 1.5m/s. Knowing that L=600mm, determine (a) the angle that the cord with the vertical (b) tension in the cord.

To find the angle that the cord makes with the vertical, we can use trigonometry. Since we know the length of the cord, L, and the radius of the circle, we can find the angle.

Given:
- Mass of the ball, m = 2 kg
- Speed of the ball, v = 1.5 m/s
- Length of the cord, L = 600 mm = 0.6 m

Let's assume the angle that the cord makes with the vertical is θ.

(a) Finding the angle θ:
In a horizontal circular motion, the tension in the cord provides the centripetal force required to keep the ball in circular motion.

The centripetal force, Fc, is given by:
Fc = mv² / r

Where m is the mass of the ball, v is the speed of the ball, and r is the radius of the circle.

Since we are given the mass (m) and speed (v) of the ball, and we need to find the radius (r), we can rearrange the formula to solve for r:
r = mv² / Fc

Now, if we draw a right triangle with the vertical as the height and the cord as the hypotenuse, the angle θ will be the angle between the height and the hypotenuse.

Using trigonometry, we can express the height of the triangle in terms of the angle θ and the length of the cord (L):
height = L * cos(θ)

Substituting this value for the radius (r) in the equation r = mv² / Fc, we get:
L * cos(θ) = mv² / Fc

Now, solving for cos(θ):
cos(θ) = (mv²) / (Fc * L)

Substituting the known values:
cos(θ) = (2 kg * (1.5 m/s)²) / (Fc * 0.6 m)

Now, we need to determine the centripetal force, Fc.

The centripetal force is provided by the tension in the cord, so Fc is equal to the tension in the cord.

Therefore, we need to find the tension in the cord.

(b) Finding the tension in the cord:
The tension in the cord, T, can be found using the formula for the centripetal force.

Fc = T

Substituting the known values into the formula:
Fc = mv² / r = m * (1.5 m/s)² / r

Now, we can substitute this value for Fc in the previous equation for cos(θ):
cos(θ) = (2 kg * (1.5 m/s)²) / (m * (1.5 m/s)² / r * 0.6 m)

Simplifying further, we get:
cos(θ) = (2 * 1.5² * r) / (1.5² * 0.6)

Now, we can solve for cos(θ):
cos(θ) = (4.5 * r) / 1.35

To find the angle θ, we can take the inverse cosine of both sides:
θ = cos^(-1)((4.5 * r) / 1.35)

Finally, substitute the value of r (which is equal to the length of the cord, L) and calculate θ.

Note: Make sure to convert the angle from radians to degrees if needed.