A 0.13 kg meter stick is held perpendicular to a wall by a 2.6 m string going from the wall to the far end of the stick.
(a) Find the tension in the string.
_________N
(b) If a shorter string is used, will its tension be greater than, less than, or the same as that found in part (a)?
_greater than
_less than
_the same as
(c) Find the tension in a 1.9 m string.
________N
I am not too sure where to begin and if anybody could walk me through the problem, it would be greatly appreciated!!
Thank you:)
You know the angle from the dimensions. Sum moments about the point at the wall on the stick, as well sum of vertical forces equals zero, and the sum of horizontal forces is zero. Remember that tension causes two force components, one horizontal, one vertical.
Can you walk me through the steps because I am unclear of how to use the distance...
Thanks!
Sure! Let's break down the problem step by step:
Given information:
- Mass of the meter stick (m) = 0.13 kg
- Length of the string (L) = 2.6 m
- Length of the shorter string (L') = 1.9 m
(a) To find the tension in the string, we can begin by calculating the torque or moment about the point where the string attaches to the wall. Since the meter stick is held perpendicular to the wall, the angle between the stick and the wall is 90 degrees.
Step 1: Calculate the weight of the meter stick.
The weight (force due to gravity) acting on the stick can be calculated as the product of mass and acceleration due to gravity:
Weight = m * g
Where:
m = mass of the meter stick = 0.13 kg
g = acceleration due to gravity = 9.8 m/s^2
Step 2: Calculate the torque (moment) about the wall point.
The torque (moment) is the product of the perpendicular distance from the point of rotation to the line of action of the force and the magnitude of the force.
Torque = (force) * (perpendicular distance)
In this case, the force causing the torque is the weight of the meter stick, and the perpendicular distance is the length of the stick.
Torque = Weight * Length
Step 3: Equate the torque to the tension in the string.
Since the tension in the string is responsible for balancing the torque, we can equate the two:
Tension = Torque / Length
Substituting the values we calculated earlier:
Tension = (Weight * Length) / Length
(b) To determine whether the tension in the shorter string (L') will be greater than, less than, or the same as the tension in part (a), we can analyze the equation for tension.
From the equation:
Tension = (Weight * Length) / Length
We can see that the tension is directly proportional to the weight and inversely proportional to the length of the string. Therefore, if the length of the string decreases (as in the case of the shorter string), the tension will increase, given that the weight remains the same.
So, the tension in the shorter string will be greater than the tension in part (a).
(c) To find the tension in the 1.9 m string, we can use the same equation as in part (a).
Tension = (Weight * Length) / Length
Substituting the new length (L') into the equation:
Tension = (Weight * 1.9 m) / 1.9 m
Since the length cancels out, the tension in the 1.9 m string will be the same as in part (a).
I hope this helps! Let me know if you have any further questions.