A uniform bar length of 2.0m and weight 1000 N has its center of gravity at its center. The bar is pivoted 0.5m from the right, and supports a weight of 200N on the opposite end (left end). What is the weight needed at right end of the bar to balance the bar?

800 N

To find the weight needed at the right end of the bar to balance it, we need to set up an equation based on the principle of moments.

Moments are calculated as the product of the weight (force) and the distance from the pivot point. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.

In this case, the clockwise moments are caused by the weight of the bar on the left side, and the counterclockwise moment is caused by the weight at the right end.

Given:
- Length of the bar = 2.0m
- Weight of the bar = 1000N
- Distance of the pivot from the right end = 0.5m
- Weight on the left end = 200N

Let's denote the weight needed at the right end as x.

Now, we can set up the equation:

Clockwise moments = Counterclockwise moments

(200N * 2.0m) = (x * 0.5m)

400Nm = 0.5x

To solve for x, divide both sides of the equation by 0.5:

x = 400Nm / 0.5m

x = 800N

Therefore, a weight of 800N is needed at the right end of the bar to balance it.

To find the weight needed at the right end of the bar to balance it, we can use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of clockwise moments about any point must be equal to the sum of counterclockwise moments about the same point.

First, let's calculate the moment caused by the weight on the left end of the bar.

Moment = Weight × Distance

The weight on the left end of the bar is 200N, and the distance from the right pivot point is 2.0m - 0.5m = 1.5m (since the bar is 2.0m long and pivoted 0.5m from the right). So the moment caused by the weight on the left end is:

Moment_left = 200N × 1.5m = 300 Nm

Next, we can calculate the moment needed to balance the bar.

Since the center of gravity is at the center of the bar, the weight of the bar itself can be considered as acting at that point. The weight of the bar is 1000N, and the distance from the right pivot point to the center of gravity is 1.0m. So the moment caused by the weight of the bar is:

Moment_bar = 1000N × 1.0m = 1000 Nm

Now, to balance the bar, the sum of clockwise moments and the sum of counterclockwise moments must be equal. Thus, we need to find the weight at the right end of the bar.

Since the bar is in equilibrium, the sum of all the clockwise moments must be equal to the sum of all the counterclockwise moments.

Clockwise Moments = Moments caused by weight on the right end

Counterclockwise Moments = Moment_left + Moment_bar

Therefore:

Moments caused by weight on the right end = Moment_left + Moment_bar

Moments caused by weight on the right end = 300 Nm + 1000 Nm

Moments caused by weight on the right end = 1300 Nm

Finally, we divide the total moments caused by the weight on the right end by the distance from the right pivot point to find the weight needed at the right end to balance the bar.

Weight_needed = Moments caused by weight on the right end / Distance

Weight_needed = 1300 Nm / 0.5m

Weight_needed = 2600 N

Hence, a weight of 2600 Newtons is needed at the right end of the bar to balance it.

600 N