a uniform rod 100cm long and weighing 50N is supported on a horizontal position on a fulcrum which weights of 80N and 100N suspended on its ends. compute the position of the fulcrum
fulcurm force: sum of weights: 230N
sum moments about the 100N end
50N*50cm+80N*100cm-230L=0
solve for L, the distance from the 100N end
The word "which" in your question should probably be "with". Let x be the distance, in cm, of the fulcrum from the end with the 80 N weight.
Since there is equilibrium, the total moment about the fulcrum is zero, and
80 x - 100(100 - x) + 50*(50 - x) = 0
130 x = 10,000 -2500 = 7500
x = 57.7 cm
Why did the fulcrum go on a diet? Because it wanted to find its balanced position! Let's figure out where it ended up.
We are given a uniform rod with a length of 100 cm (or 1 meter) and a weight of 50 N. Now, with weights of 80 N and 100 N suspended on the ends, we need to find the position of the fulcrum.
To determine the position of the fulcrum, we use the concept of torque. The torque is the product of the weight and the distance from the fulcrum.
Let's call the distance from the fulcrum to the 80 N weight "x" and the distance from the fulcrum to the 100 N weight "100 - x" (since the total length of the rod is 100 cm).
Since the rod is in equilibrium, the sum of the torques on both sides of the fulcrum should be equal:
Torque on the left side = Torque on the right side
(80 N) * x = (100 N) * (100 cm - x)
Now, let's convert the measurements to SI units:
(80 N) * x = (100 N) * (1 m - 0.01 m - x)
Simplifying the equation:
80x = 100 - 100x
Combining like terms:
80x + 100x = 100
180x = 100
Dividing both sides by 180:
x = 100/180
Now, let's compute the value:
x = 0.5556 meters
Therefore, the fulcrum is located approximately 0.5556 meters from the end where the 80 N weight is suspended.
To find the position of the fulcrum, we need to determine the distance at which it should be placed to balance the rod.
Let's assume the position of the fulcrum is x cm away from one end of the rod.
The weight of the fulcrum itself (80N) can be considered as acting at the center of the fulcrum. Therefore, its weight does not contribute to the torque produced.
The 100N weight at one end of the rod is acting on a lever arm of (100 - x) cm, and the 50N weight of the rod itself is acting on a lever arm of (50/2 = 25) cm.
The 50N weight acts at the center of mass of the rod, which is in the middle. Hence, the lever arm is half of the total rod length.
The 100N weight at the other end of the rod is acting on a lever arm of x cm.
Since the rod is in equilibrium, the sum of the clockwise and counterclockwise torques must be equal:
100N * (100 - x) = 50N * 25 + 100N * x
Simplifying this equation:
10000 - 100N*x = 1250N + 100N*x
Combining like terms:
200N*x = 8750N
Dividing both sides by 200N:
x = 8750N / 200N
Simplifying:
x = 43.75 cm
Therefore, the fulcrum should be placed approximately 43.75 cm away from one end of the rod to balance it.
To calculate the position of the fulcrum, we can make use of the principle of moments. The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
In this scenario, let's assume that the fulcrum is located at a distance of 'x' cm from one end of the rod. Therefore, the distance from the other end of the rod to the fulcrum would be (100 - x) cm.
The moment of a force is calculated by multiplying the force by the distance from the fulcrum. So, the moments of the weights can be written as follows:
Clockwise moments:
80N * (100 - x) cm
Anticlockwise moments:
100N * (x) cm
Since the rod is in rotational equilibrium, the clockwise moments should be equal to the anticlockwise moments. Thus, we can set up an equation:
80N * (100 - x) cm = 100N * (x) cm
To solve for 'x', we can simplify the equation:
8000 - 80x = 100x
Combine like terms:
180x = 8000
Divide both sides by 180:
x = 44.44 cm
Therefore, the fulcrum should be placed approximately 44.44 cm from one end of the rod to achieve rotational equilibrium.