Ball hanging from ceiling

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Using trigonometry, we can calculate the tension to be 16.66N. The horizontal component of the tension must balance the force pulling the ball aside. Using trigonometry again, we can calculate the force to be 9.03N. Therefore, the force holding the ball in position is 9.03N and the tension in the string is 16.66N. In summary, the force holding the ball in position is 9.03N and the tension in the string is 16.66N.
  • #1
lbutscha
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A 1.7-kg ball tied to a string fixed to the ceiling is pulled to one side by a force to an angle of 33.9° from the ceiling. Just before the ball is released and allowed to swing back and forth, (a) how large is the force that is holding the ball in position and (b) what is the tension in the string?



The Attempt at a Solution



I tried 16.66N for the force part a because I thought it would be the mass*gravity, but that's not right.
 
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  • #2
The sum of all the forces of the ball must be 0. This is true for both the vertical and the horizontal components. There is the force of gravity (vertical), the force that´s pulling the ball aside (horizontal) and the tension in the string which has both a vertical and a horizontal component.
Answer (b) first. The vertical component of the tension of the string should balance the gravitational force on the ball
 
  • #3
For part b, I tried 28.2N for the tension because I thought it would be the force holding the ball in position divided by the cosine of the angle, but that's not right either.

I would approach this problem by first drawing a free body diagram of the ball. This would help me visualize all the forces acting on the ball and their directions. From the given information, I can see that there are two forces acting on the ball - the force of gravity and the tension force from the string.

To find the force holding the ball in position, I would use the equation F = mg, where m is the mass of the ball and g is the acceleration due to gravity. Plugging in the values given, I get F = (1.7 kg)(9.8 m/s^2) = 16.66 N. This means that the force holding the ball in position is equal to its weight.

For part b, to find the tension in the string, I would use the equation F = Tcosθ, where T is the tension in the string and θ is the angle between the string and the vertical direction. Plugging in the values given, I get T = (16.66 N)/cos(33.9°) = 20.2 N. This means that the tension in the string is greater than the force holding the ball in position, as the string needs to provide enough force to counteract both the weight of the ball and the force pulling it to one side.

In conclusion, the force holding the ball in position is 16.66 N and the tension in the string is 20.2 N. These values are necessary to keep the ball in its initial position before it is released and allowed to swing back and forth.
 

1. What causes a ball to hang from the ceiling?

The ball is hanging from the ceiling due to the force of gravity. Gravity pulls the ball downwards towards the center of the Earth, and since the ceiling is preventing it from falling, the ball remains suspended in the air.

2. How does a ball hanging from the ceiling demonstrate Newton's laws of motion?

Newton's first law of motion states that an object at rest will remain at rest unless acted upon by an external force. In the case of the ball hanging from the ceiling, the ball is at rest until the force of gravity acts upon it. This demonstrates Newton's first law as the ball remains stationary until an external force (gravity) is applied.

3. Why does the ball not fall to the ground when it is hanging from the ceiling?

The ball does not fall to the ground because of the tension force in the string or wire holding it up. The tension force is equal and opposite to the force of gravity acting on the ball, keeping it suspended in the air.

4. How does the height of the ceiling affect the hanging ball?

The height of the ceiling does not have a significant effect on the hanging ball unless it is low enough for the ball to touch it. In this case, the ball will experience a normal force from the ceiling, in addition to the force of gravity and tension force, and may change its position or motion.

5. Is there a limit to how heavy of a ball can be hung from the ceiling?

Yes, there is a limit to how heavy of a ball can be hung from the ceiling. The strength of the material holding the ball (such as the string or wire) and the strength of the ceiling itself will determine the maximum weight that can be suspended. Exceeding this weight limit could result in the ball falling and potentially causing damage or injury.

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