An horizontal metre rule PQR is fixed at P. A force of 5N is placed at the end R to keep the metre rule in equilibrium .If PQ is 40cm. Calculate the tension in the string.
To find the tension in the string, we can use the principle of moments. The principle states that for an object to be in equilibrium, the sum of clockwise moments about a point must be equal to the sum of counterclockwise moments about the same point. Let's choose point P as our point of interest.
Let T be the tension in the string, which creates a clockwise moment about point P. The force of 5N at point R creates a counterclockwise moment about point P.
Clockwise moment: T × PQ = T × 0.40 m
Counterclockwise moment: 5N × PR = 5N × (PQ + QR) = 5N × (0.40 m + 0.60 m) = 5N × 1.00 m
For the meter rule to be in equilibrium, the clockwise and counterclockwise moments must be equal:
T × 0.40 m = 5N × 1.00 m
T = (5N × 1.00 m) / 0.40 m
T = 12.5 N
The tension in the string is 12.5 N.
To calculate the tension in the string, we need to consider the forces acting on the metre rule in equilibrium.
1. The weight of the metre rule acts vertically downward at its center of gravity (at the 20 cm mark).
2. The force at point R acts horizontally to the right, towards point Q.
Since the metre rule is in equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point. Let's choose point P as the reference point since it is fixed.
The weight of the metre rule contributes to the anticlockwise moment, while the force at point R contributes to the clockwise moment.
Let's calculate the moments:
The weight of the metre rule = Weight * distance from P
Weight = mass * acceleration due to gravity = (mass in kg) * 9.8 m/s²
The distance from P to the center of gravity = 20 cm = 0.2 m
Now, let's calculate the weight:
Weight = mass * acceleration due to gravity = (mass in kg) * 9.8 m/s²
Given that the acceleration due to gravity is approximately 9.8 m/s².
Now, let's calculate the moments:
Moment due to weight = weight * distance from P
Moment due to force at R = force at R * distance from P
Since the moments are equal:
Moment due to weight = Moment due to force at R
Therefore,
weight * distance from P = force at R * distance from P
mass * acceleration due to gravity * distance from P = force at R * distance from P
mass * acceleration due to gravity = force at R
Mass is given in kg, and acceleration due to gravity is 9.8 m/s².
Let's calculate the tension in the string:
Force at R = mass * acceleration due to gravity
Force at R = 5 N
Therefore, the tension in the string is 5 N.
To calculate the tension in the string, we need to consider the equilibrium of forces acting on the horizontal meter rule.
In this scenario, the meter rule is kept in equilibrium by the force applied at point R. We can assume that the force applied at R acts vertically upward, as there is no horizontal force acting on the system.
Let's break down the forces acting on the meter rule:
1. Weight of the meter rule (acting at its center of gravity): This force acts vertically downward and can be considered as acting at the midpoint of PQ. Since the meter rule is in equilibrium, the weight must be balanced by the force applied at R.
2. Force applied at R: This force acts vertically upward to balance the weight of the meter rule. The magnitude of this force is given as 5N.
To find the tension in the string, we need to determine the weight of the meter rule. Since the meter rule is at equilibrium, the weight can be considered as acting at the midpoint of PQ. We can calculate it as follows:
Weight of the meter rule = Mass x Gravitational acceleration
Now, assuming the meter rule is uniform and has a mass of M kg:
Weight of the meter rule = M kg x 9.8 m/s^2
To calculate the mass of the meter rule, we need to convert the length from cm to meters:
Length of PQ = 40 cm = 0.4 m
The mass of the meter rule can be found using the formula:
Mass = Density x Volume
Since the meter rule is uniform, its volume can be calculated as the product of its length, width, and thickness. Let's assume the width and thickness are both negligible compared to the length.
The width and thickness are not given, so we cannot directly calculate the mass of the meter rule. However, we can assume they are small enough to have a negligible effect on the tension in the string.
Therefore, we can approximate the mass of the meter rule as zero (0 kg). This means the tension in the string is equal to the weight of the meter rule, which is also zero.
Hence, the tension in the string is 0 N.