A uniform meter rule on a knife edge at the 60cm Mark has a mass of 70g hung at the 90cm mark x hung at the 20cm mark to balance it horizontally
1 sketch the set up
2 calculate x
need mass of ruler
1. To sketch the set up, we can divide the meter rule into three sections: the left side (0-20 cm), the middle section (20-60 cm), and the right side (60-100 cm).
At the 90 cm mark, we hang a 70 g mass downward. At the 20 cm mark, we hang an unknown mass, x, downward. Both masses are connected by strings or threads. The meter rule is balanced horizontally, which means the torque (moment) on one side is equal to the torque on the other side.
----------------------[x]-----[70 g]------------------
0 20 60 100 cm
2. To calculate x, we need to consider the balance of torques.
The torque of an object is given by the formula:
Torque = Force × Distance
On the left side (0-20 cm), the torque is zero since there is no weight hanging from that side.
On the right side (60-100 cm), the torque is given by:
Torque_right = Force × Distance
= 70 g × (100 cm - 60 cm) [distance from 60 to 100 cm is 40 cm]
= 70 g × 40 cm
On the middle section (20-60 cm), the torques on both sides are equal, so we can set them equal to each other:
Torque_left = Torque_right
The torque on the left side is given by:
Torque_left = Force × Distance
= x × (20 cm - 0 cm) [distance from 0 to 20 cm is 20 cm]
= x × 20 cm
Setting Torque_left equal to Torque_right, we have:
x × 20 cm = 70 g × 40 cm
To solve for x, we need to convert the mass from grams to kilograms:
70 g = 70 g / 1000 = 0.07 kg
Now we can solve for x:
x × 20 cm = 0.07 kg × 40 cm
Simplifying:
20x cm = 0.07 kg × 40 cm
Dividing both sides by 20 cm:
x = (0.07 kg × 40 cm) / 20 cm
Simplifying further:
x = 0.07 kg × 2
x = 0.14 kg
Therefore, x = 0.14 kg.
To sketch the setup, draw a straight line to represent the meter rule. Label the 0cm mark on the left end and the 100cm mark on the right end. Place a knife edge at the 60cm mark. Next, draw a vertical line at the 90cm mark and hang a mass of 70g from it. Finally, draw another vertical line at the 20cm mark and hang an unknown mass x from it. Make sure the meter rule is balanced horizontally, with the knife edge acting as the pivot point.
To calculate x, we need to ensure that the meter rule is balanced horizontally. This means that the clockwise moments must be equal to the counterclockwise moments. The moment of a force about a pivot point is given by the formula:
Moment = Force × perpendicular distance from the pivot point.
In this case, let's consider the clockwise moments:
Clockwise moment = 70g × (90 - 60)cm = 70g × 30cm.
Now, let's consider the counterclockwise moments:
Counterclockwise moment = x × (20 - 60)cm = x × (-40)cm.
Since the meter rule is balanced, the clockwise moments must be equal to the counterclockwise moments:
70g × 30cm = x × (-40)cm.
To solve for x:
70g × 30cm = -40x cm.
Rearranging the equation:
x = (70g × 30cm) / (-40cm).
Calculating the value of x:
x = - (70g × 30cm) / (40cm).
x = - 52.5g.
Therefore, x is equal to -52.5g.