Question

A uniform rod is 2.20 m long and has mass 1.80 kg. A 1.20 kg clamp is attached to the rod. How far should the center of gravity of the clamp be from the left-hand end of the rod in order for the center of gravity of the composite For related problem-solving tips and strategies, you object to be 1.30 m from the left-hand end of the rod? may want to view a Video Tutor Solution of Express your answer with the appropriate units.

Answer 1

To find the distance of the center of gravity of the clamp from the left end of the rod, we can use the principle of moments or torques. The center of gravity should be approximately 1.65 m from the left end of the rod.

Step-by-step explanation:

To determine the distance that the center of gravity of the clamp should be from the left-hand end of the rod, we can use the principle of moments or torques. The center of gravity of the system should be 1.30 m from the left-hand end of the rod. Let's assume that the distance between the clamp and the left-hand end is x. The torque about the left end can be calculated as the weight of the rod multiplied by its distance from the left end (2.2 m - x), plus the weight of the clamp multiplied by its distance from the left end (x).

The torque about the left end should be equal to zero because the system is in equilibrium. Therefore, we have:

(1.8 kg)(9.8 m/s^2)(2.2 m - x) + (1.2 kg)(9.8 m/s^2)(x) = 0

Simplifying the equation, we get:

3.96 m - 1.8x + 1.2x = 0

2.4x = 3.96

x = 1.65 m

So, the center of gravity of the clamp should be approximately 1.65 m from the left-hand end of the rod.

Answer 2

To find the location of the center of gravity of the clamp on a uniform rod, we can use the principle of moments. By balancing the moments due to the clamp and the rod, we can calculate the distance between the left-hand end of the rod and the center of gravity of the clamp. In this case, the center of gravity of the clamp should be 1.02 m from the left-hand end of the rod.

Step-by-step explanation:

To find the location of the center of gravity of the clamp on the uniform rod, we can use the principle of moments. The center of gravity is the point at which the gravitational forces can be considered to act. Let's assume that the distance between the left-hand end of the rod and the center of gravity of the clamp is x. The center of gravity of the rod itself is located at its midpoint, which is 2.20 m / 2 = 1.10 m from the left-hand end of the rod.

To balance the composite object, the sum of the moments about any point must be zero. We can take moments about the left-hand end of the rod. The moment due to the clamp can be calculated as the product of its mass and its distance from the point of rotation (0.5 kg * x). The moment due to the rod can be calculated as the product of its mass (1.80 kg) and its distance from the point of rotation (1.10 m).

Setting up the equation, we have: (0.5 kg * x) + (1.80 kg * 1.10 m) = (1.20 kg * 1.30 m). Solving for x, we find that x = (1.20 kg * 1.30 m - 1.80 kg * 1.10 m) / 0.5 kg = 1.02 m.