A 3.0-m rod is pivoted about its left end. A force of 6.0 N is applied perpendicular to the rod at a distance of 1.2m from the pivot causing a CCW torque, and a force of 5.2N is applied at the end of the rod 3.0m from the pivot. the 5.2N is at an angle of 30 degrees to the rod and causes a CW torque. What is the net torque about the pivot?
(6.0*1.2) - (5.2*3.0)*sin 30
= 7.2 - 7.8 = -0.6 Newton meters
To find the net torque about the pivot, we need to calculate the torques caused by each force and then determine their sum.
The torque caused by a force on a rigid body is given by the equation:
τ = F * r * sin(θ)
Where:
- τ is the torque
- F is the force applied
- r is the perpendicular distance from the pivot point to the line of action of the force
- θ is the angle between the force and the lever arm (perpendicular distance)
Let's calculate the torque caused by each force separately and then sum them up.
1. Torque caused by the 6.0 N force:
- F = 6.0 N
- r = 1.2 m (perpendicular distance from the pivot to the force)
- θ = 90 degrees (since the force is applied perpendicular to the rod)
τ1 = 6.0 N * 1.2 m * sin(90 degrees)
τ1 = 6.0 N * 1.2 m * 1
τ1 = 7.2 N*m
2. Torque caused by the 5.2 N force:
- F = 5.2 N
- r = 3.0 m (perpendicular distance from the pivot to the force)
- θ = 30 degrees (angle between the force and the lever arm)
τ2 = 5.2 N * 3.0 m * sin(30 degrees)
τ2 = 5.2 N * 3.0 m * 0.5
τ2 = 7.8 N*m
Now, to find the net torque, we sum up the individual torques:
Net torque = τ1 + τ2
Net torque = 7.2 N*m + 7.8 N*m
Net torque = 15.0 N*m
Therefore, the net torque about the pivot is 15.0 N*m.
To find the net torque about the pivot, we need to calculate the torques caused by each force and then add them together.
Torque is given by the equation: Torque = Force * Distance * sin(θ)
Where:
- Force is the magnitude of the force applied
- Distance is the perpendicular distance from the pivot to the line of action of the force
- θ is the angle between the force and the lever arm (distance)
Given information:
Force 1 = 6.0 N
Distance 1 = 1.2 m
Force 2 = 5.2 N
Distance 2 = 3.0 m
θ = 30 degrees
First, let's calculate the torque caused by Force 1:
Torque 1 = Force 1 * Distance 1 * sin(θ)
= 6.0 N * 1.2 m * sin(90 degrees)
= 7.2 N⋅m
Next, let's calculate the torque caused by Force 2:
Torque 2 = Force 2 * Distance 2 * sin(θ)
= 5.2 N * 3.0 m * sin(30 degrees)
= 7.8 N⋅m
The net torque about the pivot is the sum of the torques:
Net Torque = Torque 1 + Torque 2
= 7.2 N⋅m + 7.8 N⋅m
= 15 N⋅m
Therefore, the net torque about the pivot is 15 N⋅m.