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?

To find the tension in the cord, we can begin by calculating the centripetal force acting on the ball. The centripetal force is given by the equation:

F = m * a

Where:
F is the centripetal force
m is the mass of the ball
a is the centripetal acceleration

In this case, we are given the mass of the ball as 800 grams (or 0.8 kg) and the tangential speed as 10 meters per second. We know that the centripetal acceleration, a, can be calculated using the formula:

a = v^2 / r

Where:
v is the tangential speed
r is the radius of the circle

Now, let's calculate the centripetal acceleration:

a = (10 m/s)^2 / 1.50 m
a = 100 m^2/s^2 / 1.50 m
a ≈ 66.67 m/s^2

Now that we have the centripetal acceleration, we can calculate the centripetal force:

F = m * a
F = 0.8 kg * 66.67 m/s^2
F ≈ 53.34 N

So, the tension in the cord must be approximately 53.34 Newtons.

To find the angle that the cord makes with the horizontal, we can use trigonometry. The tension force in the cord acts as the vertical component, and the weight of the ball acts as the horizontal component. The angle between the cord and the horizontal can be given by:

θ = arctan(tension / weight)

Since we know the tension in the cord is 53.34 N, we need to find the weight of the ball. The weight can be calculated using the formula:

weight = mass * gravity

Assuming the acceleration due to gravity is 9.8 m/s^2, we can calculate the weight:

weight = 0.8 kg * 9.8 m/s^2
weight ≈ 7.84 N

Now, let's find the angle:

θ = arctan(53.34 N / 7.84 N)
θ ≈ arctan(6.8)

Using a calculator, we find that θ ≈ 81.68 degrees.

Therefore, the cord makes an angle of approximately 81.68 degrees with the horizontal.