a 800 gram ball at the end of a cord is whirled in an almost horizontal circle of radius 1.50 meters. its tangential speed in the circle is 10 meters per second. What must be the tension in the cord? What angle does the cord make with the horizontal?

12.33

1,88

To find the tension in the cord, we can use the concept of centripetal force. The centripetal force is the force directed toward the center of the circular motion that keeps an object moving in a circle.

The formula for centripetal force is:

F = (m * v^2) / r

where:
F is the centripetal force,
m is the mass of the object,
v is the tangential speed, and
r is the radius of the circle.

Let's calculate the centripetal force using the given values:
m = 800 grams = 0.8 kg (since 1 kg = 1000 grams)
v = 10 m/s
r = 1.50 meters

Plugging in the values into the formula:

F = (0.8 kg * (10 m/s)^2) / 1.50 meters

F = (0.8 kg * 100 m^2/s^2) / 1.50 meters

F ≈ 0.8 kg * 66.67 m^2/s^2

F ≈ 53.34 N

Therefore, the tension in the cord is approximately 53.34 Newtons.

To find the angle the cord makes with the horizontal, we can use trigonometry. In this case, the tension in the cord acts as the vertical component of the tension, and the weight of the ball (mg) acts as the horizontal component of the tension.

Let's define the angle as θ.

Therefore, the equation for the vertical component of tension is:

T * sin(θ) = mg

And the equation for the horizontal component of tension is:

T * cos(θ) = F (centripetal force)

We already know the value of F (53.34 N) from the previous calculation.

From the vertical component equation, we have:

T * sin(θ) = mg

And from the horizontal component equation, we have:

T * cos(θ) = 53.34 N

Dividing the two equations:

(T * sin(θ)) / (T * cos(θ)) = mg / 53.34 N

simplifying:

tan(θ) = mg / 53.34 N

Now, we can substitute the values:

m = 0.8 kg
g = 9.8 m/s^2 (acceleration due to gravity)

tan(θ) = 0.8 kg * 9.8 m/s^2 / 53.34 N

tan(θ) ≈ 0.147

Now, we can take the inverse tangent (arctan) of both sides to find the angle θ:

θ ≈ arctan(0.147)

θ ≈ 8.47 degrees

Therefore, the angle the cord makes with the horizontal is approximately 8.47 degrees.