a light uniform meter rule PT pivoted at Q the 30cm mark has a block of mass 1.5kg suspended at the 80cm mark. The meter rule is maintained at equilibrium by a string attached at the point R the 50cm mark. What is the tension in the string?
the block is 50 cm from the pivot
the string is 20 cm from the pivot
the tension is ... 1.5 * g * (50 / 20)
WE WANT THE CALCULATION
To find the tension in the string, we need to consider the torque balance for the meter rule in equilibrium.
1. Calculate the weight of the block suspended at the 80cm mark:
Weight = mass * acceleration due to gravity
= 1.5 kg * 9.8 m/s^2
= 14.7 N
2. Determine the distance of the weight from the pivot point Q:
Distance = 80 cm - 30 cm
= 50 cm
3. Determine the distance of the tension force from the pivot point R:
Distance = 50 cm - 50 cm
= 0 cm
4. Set up the torque balance equation:
Torque due to weight = Torque due to tension
Weight * Distance from pivot Q = Tension * Distance from pivot R
14.7 N * 50 cm = Tension * 0 cm
The distance of the tension force from the pivot is 0 cm since the tension force acts at the pivot point itself.
5. Solve for the tension:
Tension = (14.7 N * 50 cm) / 0 cm
= 0 N
Therefore, the tension in the string is 0 N.
To find the tension in the string, we can use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
In this case, we have two forces acting on the meter rule - the weight of the meter rule itself and the weight of the block hanging from it.
Step 1: Calculate the moment due to the weight of the meter rule:
The weight of the meter rule can be considered to act at its center of gravity, which is at the midpoint. The weight acts vertically downward at a distance of 50 cm from the pivot point Q. Since it is a uniform meter rule, we can assume its weight acts at the center of gravity.
Moment due to the weight of the meter rule = Weight of the meter rule x Distance from the pivot
= (Weight of the meter rule) x (Distance of the center of gravity from the pivot)
= (Weight of the meter rule) x 50 cm
Step 2: Calculate the moment due to the weight of the block:
The weight of the 1.5 kg block acts vertically downward at a distance of 30 cm from the pivot point Q.
Moment due to the weight of the block = Weight of the block x Distance from the pivot
= (Weight of the block) x (Distance of the block from the pivot)
= (Weight of the block) x 30 cm
Step 3: Set up the equation for equilibrium by taking moments about the pivot point Q:
Sum of clockwise moments = Sum of anticlockwise moments
(Tension in the string) x (Distance of the string from the pivot) = Moment due to the weight of the meter rule + Moment due to the weight of the block
Let's say the distance of the string from the pivot point Q is 'd' cm.
(Tension in the string) x d = (Weight of the meter rule) x 50 cm + (Weight of the block) x 30 cm
Step 4: Substitute the values and solve for tension in the string:
Weight of the meter rule = (Mass of the meter rule) x (Acceleration due to gravity)
= (Mass of the meter rule) x 9.8 m/s^2
Weight of the block = (Mass of the block) x (Acceleration due to gravity)
= (Mass of the block) x 9.8 m/s^2
Substitute these values into the equation and solve for (Tension in the string).
Please note that the mass of the meter rule and block need to be converted to kilograms and the length should be converted to meters in order to obtain the tension in newtons.