The 600-N ball shown is suspended on a string AB and rests against the frictionless vertical wall. The string makes an angle of 30 $\degree$ with the wall. The line AB goes through the center of the ball, and the contact point with the wall is at the same vertical height as the center of the ball. The magnitude of the tension in the string is:
A) 300 N
B) 520 N
C) 690 N
D) 1200 N
E) none of these

Question

The 600-N ball shown is suspended on a string AB and rests against the frictionless vertical wall. The string makes an angle of 30 $\degree$ with the wall. The line AB goes through the center of the ball, and the contact point with the wall is at the same vertical height as the center of the ball. The magnitude of the tension in the string is: 
A) 300 N 
B) 520 N 
C) 690 N 
D) 1200 N 
E) none of these

Quizplus · Accepted Answer

First, we draw a force diagram of the ball.

![image.png](attachment:image.png)

Since the wall is frictionless, the only forces acting on the ball are the force due to gravity of 600 N downwards and the tension force of the string cord AB.

We can break the tension force into two components: one parallel to the wall and one perpendicular to the wall.

![image-2.png](attachment:image-2.png)

The block is at rest, so the net force acting on it must be zero. This means the magnitude of the tension force in the horizontal direction must balance the gravitational force pulling the ball down:

Tsin30° = 600 N

Solving for T, we get:

T = 1200 N.

However, we’re not done yet! We need to make sure that this tension satisfies the vertical direction as well.

Looking at the vertical direction, we see that there’s a downward force due to gravity and an upward force from the vertical component of the tension force. The ball is not moving up or down, so these two forces must balance each other:

Tcos30° = mg

Tcos 30° = (600 N)cos(30°)

T = (600 N) / (cos30°)

T = 690 N.

Therefore, the magnitude of the tension force in the string is 690 N, which is answer choice C.

The 600-N Ball Shown Is Suspended on a String AB °\degree°

The 600-N Ball Shown Is Suspended on a String AB $\degree$