. 0.30m
....|______|_________________________
....|...../\
...|_| <-- box with unknown mass
In the figure, the meterstick's mass is 0.200 kg and the string tension is 2.50 N . The system is in equilibrium.
Find the (a) unknown mass m and (b) the upward force the fulcrum exerts on the stick.
. ....0.30m
....|______|_________________________
....|........../\
...|_| <-- box with unknown mass
I can't figure out what they mean by a string in your drawing. If it's just the box and the ruler:
Sum of torques = zero
m*9.8*.3 = .2*9.8*.2
its a yardstick on a fulcrum. on the left hand side a block is hanging from a string. I tried to submit it with a url but it would not let me so i attempted to draw it out. the length of the meterstick from the lefthand side to the fulcrum is .30m
To find the unknown mass (m) and the upward force the fulcrum exerts on the stick, we can use the concept of torque and equilibrium.
Torque is the rotational equivalent of force and is calculated by multiplying the force applied by the perpendicular distance from the axis of rotation. In this case, the axis of rotation is the fulcrum.
Let's begin by finding the unknown mass (m):
Step 1: Calculate the torque due to the box:
The torque due to the box is the product of its force (weight) and its perpendicular distance from the fulcrum. Since the string tension pulls the box vertically upward, the perpendicular distance is the length of the meterstick (0.30 m).
Torque due to the box = Force × Perpendicular Distance
Torque due to the box = m × g × 0.30 m (where g is the acceleration due to gravity and equals 9.8 m/s²)
Step 2: Calculate the torque due to the meterstick:
The torque due to the meterstick is the product of its weight (mass × g) and its perpendicular distance from the fulcrum. The perpendicular distance is half of the length of the meterstick (0.15 m).
Torque due to the meterstick = Weight of the meterstick × Perpendicular Distance
Torque due to the meterstick = (0.200 kg × 9.8 m/s²) × 0.15 m
Step 3: Set up the equilibrium condition:
In equilibrium, the sum of all the torques acting on the system must be zero.
Torque due to the box + Torque due to the meterstick = 0
m × g × 0.30 m + (0.200 kg × 9.8 m/s²) × 0.15 m = 0
Step 4: Solve for m:
Rearrange the equation and solve for m:
m × 9.8 × 0.30 + 0.200 × 9.8 × 0.15 = 0
m × 2.94 + 0.200 × 1.47 = 0
m × 2.94 = -0.200 × 1.47 (dividing both sides by 2.94)
m = (-0.200 × 1.47) / 2.94
Evaluate the expression to find the value of m.
Now, to find the upward force that the fulcrum exerts on the stick (F_fulcrum), we can use the fact that the sum of all vertical forces must also be zero in equilibrium.
Step 5: Calculate the upward force exerted by the fulcrum:
Sum of vertical forces = Force due to the box + Weight of the meterstick + F_fulcrum = 0
Substituting the known values and the calculated value of m, solve for F_fulcrum.
This allows us to find both the unknown mass (m) and the upward force the fulcrum exerts on the stick (F_fulcrum).