Suppose the mass of the stick is 200 g, and a single 500-g mass is to play "solitary seesaw" at the 0-cm mark. Where should the fulcrum be located?
To determine the location of the fulcrum, we need to consider the principle of moments, which states that the total sum of clockwise moments is equal to the total sum of counterclockwise moments.
Given:
Mass of the stick = 200 g = 0.2 kg
Mass of the 500 g mass = 500 g = 0.5 kg
Let's assume the distance from the fulcrum to the 500 g mass is x cm. Therefore, the distance from the fulcrum to the 200 g stick would be (100 - x) cm, as the total length of the stick is 100 cm.
The moment of the 500 g mass can be calculated as:
Moment1 = Mass1 × Distance1 = 0.5 kg × x cm = 0.5x N·m
The moment of the 200 g stick can be calculated as:
Moment2 = Mass2 × Distance2 = 0.2 kg × (100 - x) cm = 0.2(100 - x) N·m
According to the principle of moments, Moment1 = Moment2:
0.5x = 0.2(100 - x)
Simplifying the equation:
0.5x = 20 - 0.2x
0.5x + 0.2x = 20
0.7x = 20
x = 20 / 0.7
Calculating the value of x:
x ≈ 28.57 cm
Therefore, the fulcrum should be located approximately 28.57 cm away from the 500 g mass, towards the 0-cm mark.
To determine the location of the fulcrum, we need to achieve equilibrium on the seesaw. Equilibrium means that the sum of the torques (moments) on both sides of the fulcrum is equal.
In this case, we have two torques acting on the seesaw: the torque from the stick and the torque from the 500g mass.
The torque (τ) is calculated as the product of the force (F) and the perpendicular distance (d) from the point of rotation (fulcrum) to the line of action of the force. Mathematically, τ = F * d.
Let's assume the location of the fulcrum as distance x from the 0-cm mark. The torque from the 200g stick is given by τ1 = (0.2 kg) * (9.8 m/s^2) * (x cm).
Similarly, the torque from the 500g mass is given by τ2 = (0.5 kg) * (9.8 m/s^2) * (x - 0 cm).
To achieve equilibrium, the sum of the torques should be zero. So, we can set up the equation:
0 = τ1 + τ2
0 = (0.2 kg) * (9.8 m/s^2) * (x cm) + (0.5 kg) * (9.8 m/s^2) * (x - 0 cm)
Now, we can solve this equation to find the value of x, which represents the location of the fulcrum:
0 = (0.2 kg) * (9.8 m/s^2) * x + (0.5 kg) * (9.8 m/s^2) * x - (0.5 kg) * (9.8 m/s^2) * 0
Simplifying the equation:
0 = (0.2 kg + 0.5 kg) * (9.8 m/s^2) * x
0 = (0.7 kg) * (9.8 m/s^2) * x
0 = 6.86 x
Since torque cannot be zero, x must be zero.
Therefore, the fulcrum should be located at the 0-cm mark for the seesaw to be in equilibrium.
Assume L for length of stick.
Put the fulcrum at x from the 500-g mass.
The centre of gravity of the stick is at the centre, L/2, where the mass is assumed to concentrate.
Take moments about the fulcrum:
500*x=200*(L/2-x)
Solve for x in terms of L:
x=L/7