A 4 kg rock is suspended by a massless string from one end of a 7 m measuring stick. What is the weight of the measuring stick if it is balanced by a support force at the 1 m mark? The acceleration of gravity is 9.81 m/52 Answer in units of N.
To solve this problem, we need to analyze the forces acting on the measuring stick.
First, let's calculate the weight of the rock. The weight can be calculated using the formula:
Weight = mass * gravity
Weight = 4 kg * 9.81 m/s^2
Weight = 39.24 N
Since the measuring stick is balanced, the total torque on the measuring stick must be zero. The torque due to the weight of the rock can be calculated as:
Torque = weight * distance
Torque = 39.24 N * 7 m
Torque = 274.68 N·m
We want to find the support force at the 1 m mark. The distance from the support force to the center of the measuring stick is 6 m (7 m - 1 m). Therefore, the torque due to the support force can be calculated as:
Torque = support force * distance
Torque = support force * 6 m
Since the measuring stick is balanced, the torque due to the support force must be equal and opposite to the torque due to the weight of the rock:
274.68 N·m = support force * 6 m
Solving for the support force:
support force = 274.68 N·m / 6 m
support force = 45.78 N
Therefore, the weight of the measuring stick is 45.78 N.