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?

tension= centripetal force= mass*v^2/r

angle? centripetal force is horzontal, weight is vertical

tanTheta=mg/mv^2/r= rg/v^2

theta = arctan (above)

To find the tension in the cord, we need to consider the forces acting on the ball. In this case, the tension in the cord provides the necessary centripetal force to keep the ball moving in a circle.

The centripetal force can be calculated using the following formula:

F_c = (m * v^2) / r

where F_c is the centripetal force, m is the mass of the ball, v is the tangential speed, and r is the radius of the circle.

Given:
- mass of the ball (m) = 800 grams = 0.8 kg
- tangential speed (v) = 10 m/s
- radius of the circle (r) = 1.50 meters

Calculating the centripetal force:

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

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

F_c = 80 N

Therefore, the tension in the cord must be 80 Newtons.

Now, to find the angle that the cord makes with the horizontal, we can consider the right triangle formed by the horizontal component of the tension force and the weight of the ball. The vertical component of the tension force and the weight of the ball are balanced out, resulting in a net vertical force of zero.

In this triangle, the tangent of the angle (θ) can be calculated as:

tan(θ) = (horizontal component of tension) / (vertical component of tension)

tan(θ) = (tension force * sin(θ)) / (tension force * cos(θ))

tan(θ) = sin(θ) / cos(θ)

tan(θ) = (m * v^2) / (m * g)

tan(θ) = v^2 / g

where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Now, substituting the given values:

tan(θ) = (10 m/s)^2 / 9.8 m/s^2

tan(θ) = 100 / 9.8

tan(θ) ≈ 10.2

Taking the inverse tangent (tan^-1) of both sides:

θ ≈ tan^-1(10.2)

θ ≈ 83.59 degrees

Therefore, the angle that the cord makes with the horizontal is approximately 83.59 degrees.