a. The forces exerted on the ball at point b are: Tension in the thread , Weight of the ball.
b. The speed of the ball at point a is 5.0 m/s.
c. The tension in the thread at point a is 83.3 N.
d. The tension in the thread at point b is 333 N.
a. Using a dot model, draw and label all the forces exerted on the ball when it is at point b.
The dot model of the forces on the ball at point b is shown below:
+----------------+
| Tension in thread |
+----------------+
|
|
v
|
|
+-----+
| Ball |
+-----+
b. Determine the speed of the ball at point a. Show your work.
Since mechanical energy is conserved, the speed of the ball at point a will be the same as its speed at point b, which is 5.0 m/s.
c. Determine the tension in the thread at point a. Show your work.
The tension in the thread at point a is equal to the centripetal force required to keep the ball moving in a circle.
The centripetal force is given by:
F_c = mv^2/r
where:
m is the mass of the ball (20 kg)
v is the speed of the ball (5.0 m/s)
r is the radius of the circle (0.60 m)
Therefore, the tension in the thread at point a is:
F_c = (20 kg)(5.0 m/s)^2 / 0.60 m = 83.3 N
d. Determine the tension in the thread at point b. Show your work.
The tension in the thread at point b is equal to the weight of the ball plus the centripetal force required to keep the ball moving in a circle.
The weight of the ball is given by:
F_g = mg
where:
m is the mass of the ball (20 kg)
g is the acceleration due to gravity (9.81 m/s^2)
Therefore, the tension in the thread at point b is:
F_b = F_g + F_c = (20 kg)(9.81 m/s^2) + (20 kg)(5.0 m/s)^2 / 0.60 m = 3