A uniform meter stick weighing five new ins is pivoted so we can rotate about a horizontal access through one end if a. 15 kg mass is suspended 75 cm from the pivoted end what force must be applied to the free end of the meter steak to maintain it in a horizontal position
To find the force required to maintain the meter stick in a horizontal position, we can use the principle of torque. Torque is the product of force applied and the distance from the pivot point.
In this case, let's assume the meter stick is balanced horizontally (no net torque). The weight of the meter stick can be considered as acting at its center of gravity, which is the midpoint. The distance between the pivot point and the center of gravity is half the length of the meter stick, or 50 cm.
The 15 kg mass is suspended 75 cm from the pivoted end. So the distance between the pivot point and the suspended mass is 75 + 50 = 125 cm.
Now, let's calculate the torque applied by the 15 kg mass. Since torque is the product of force and distance, we have:
Torque = Force × Distance
In this case, the distance is 125 cm, so we can write:
Torque = Force × 125 cm
The weight of the 15 kg mass can be calculated using the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s². Converting the mass from kg to newtons, we have:
Weight = 15 kg × 9.8 m/s² = 147 N
To balance the torque caused by the weight of the mass, an equal and opposite torque needs to be applied at the free end of the meter stick. In this case, the distance is 50 cm, so we can write:
Torque = Force × 50 cm
Since the meter stick is balanced (no net torque), the torque applied by the weight of the mass is equal and opposite to the torque required to balance it:
Force × 125 cm = Force × 50 cm
Simplifying the equation, we find:
Force × 125 = Force × 50
Dividing both sides by Force (assuming it is not zero), we get:
125 = 50
This is not a valid equation since it does not hold true. It means that there is no force that can be applied to the free end of the meter stick to maintain it in a horizontal position while the 15 kg mass is suspended at 75 cm.