A meter stick lies along the x-axis, centered at the origin. An upward force of 6.0 N is applied at x = 30 cm, and an upward force of 8.0 N is simultaneously applied at x = −40 cm. What is the net torque on the meter stick, taking into account usual sign conventions?
The net torque on the meter stick is -2.4 Nm.
To calculate the net torque on the meter stick, we need to consider the torque contributed by each force separately and then sum them up.
The torque (τ) produced by a force (F) acting at a distance (r) from the axis of rotation is given by the equation:
τ = F * r * sin(θ)
Where θ is the angle between the force vector and the vector from the axis of rotation to the point where the force is applied.
Let's calculate the torque produced by each force:
1. Force at x = 30 cm:
The distance from the origin to x = 30 cm is 30 cm = 0.30 m. Since the force is applied upwards, the angle θ is 90 degrees.
τ1 = 6.0 N * 0.30 m * sin(90°) = 1.8 Nm
2. Force at x = -40 cm:
The distance from the origin to x = -40 cm is 40 cm = 0.40 m. Since the force is applied upwards, the angle θ is 90 degrees.
τ2 = 8.0 N * 0.40 m * sin(90°) = 3.2 Nm
Now, we can find the net torque by summing up the individual torques:
Net torque = τ1 + τ2 = 1.8 Nm + 3.2 Nm = 5.0 Nm
Therefore, the net torque on the meter stick is 5.0 Nm.
To find the net torque on the meter stick, we need to calculate the torque produced by each force applied and then sum them up. The torque produced by a force is given by the formula:
Torque = Force * Lever Arm
where the lever arm is the perpendicular distance from the axis of rotation to the line of action of the force.
In this case, the meter stick is centered at the origin, so the axis of rotation is at the center of the meter stick (x = 0 cm).
For the force of 6.0 N applied at x = 30 cm:
Lever Arm = 30 cm - 0 cm = 30 cm
Torque = 6.0 N * 30 cm = 180 Ncm
For the force of 8.0 N applied at x = -40 cm:
Lever Arm = -40 cm - 0 cm = -40 cm
Torque = 8.0 N * (-40 cm) = -320 Ncm
Note that the sign convention for torque is positive for counterclockwise and negative for clockwise torques.
Now, to find the net torque, we simply add up the torques:
Net Torque = Torque1 + Torque2
Net Torque = (180 Ncm) + (-320 Ncm)
Net Torque = -140 Ncm
So, the net torque on the meter stick is -140 Ncm.