Which produces the largest torque?
--->> 30.0 N perpendicular to the center of rotation at a radius of 1.5 m
30.0 N perpendicular to the center of rotation at a radius of 0.25 m
60.0 N perpendicular to the center of rotation at a radius of 1.0 m
60.0 N perpendicular to the center of rotation at a radius of 0.5 m
Huh?
30 * 1.5 = 45
BUT
60 * 1 = 60
ohh..that was a terrible mistake I just did
So what is the answer.
Well, if you want torque, you've come to the right bot! Let me break it down for you. Torque is the product of force and the perpendicular distance from the pivot point, also known as the radius. So, we need to find the combination that gives us the highest result.
Let's calculate the torques for each scenario:
Torque 1: 30.0 N × 1.5 m = 45.0 Nm
Torque 2: 30.0 N × 0.25 m = 7.5 Nm
Torque 3: 60.0 N × 1.0 m = 60.0 Nm
Torque 4: 60.0 N × 0.5 m = 30.0 Nm
Drumroll, please! The largest torque is produced by 60.0 N perpendicular to the center of rotation at a radius of 1.0 m, giving us a whopping 60.0 Nm of torque. So there you have it, the big winner!
To determine which produces the largest torque, we need to calculate the torque for each scenario and compare the values.
Torque is given by the formula:
Torque = Force * Radius * sin(θ)
Where:
- Force is the perpendicular force applied (given as 30.0 N or 60.0 N)
- Radius is the distance from the center of rotation to the point where the force is applied (given as 1.5 m, 0.25 m, 1.0 m, or 0.5 m)
- θ is the angle between the force and the line connecting the center of rotation to the point where the force is applied. Since the force is perpendicular to the center of rotation in all scenarios, sin(θ) is equal to 1.
Now let's calculate the torque for each scenario:
For the first option, with a force of 30.0 N and a radius of 1.5 m:
Torque = 30.0 N * 1.5 m * sin(θ) = 30.0 N * 1.5 m * 1 = 45.0 Nm
For the second option, with a force of 30.0 N and a radius of 0.25 m:
Torque = 30.0 N * 0.25 m * sin(θ) = 30.0 N * 0.25 m * 1 = 7.5 Nm
For the third option, with a force of 60.0 N and a radius of 1.0 m:
Torque = 60.0 N * 1.0 m * sin(θ) = 60.0 N * 1.0 m * 1 = 60.0 Nm
For the fourth option, with a force of 60.0 N and a radius of 0.5 m:
Torque = 60.0 N * 0.5 m * sin(θ) = 60.0 N * 0.5 m * 1 = 30.0 Nm
Comparing the torque values, we can see that the third option, with a force of 60.0 N and a radius of 1.0 m, produces the largest torque of 60.0 Nm.