Several math students are taking a break from their studies by visiting a playground. One student pushes the others on a merry-go-round. The diameter of the merry-go-round is 3.0 m, and the student pushes with a force of 50 N along the purple vector shown in the diagram. Merry-go-round showing applied force acting on an angle of 110�
What torque does the student apply?
At what angle would the student need to apply the force to achieve maximum torque?
If the student continues to push with a force of 50 N, what maximum torque could be applied?
I am not certain how the angle is applied...
torque=forceperpendiculartoRadii*Radius
so use this, and your drawing, to figure out the answers.
To find the torque applied by the student, we need to multiply the magnitude of the force (50 N) by the perpendicular distance from the line of action of the force to the axis of rotation. This distance is given by the radius of the merry-go-round (half the diameter).
1. Torque (τ) = Force (F) x Perpendicular Distance (r)
τ = 50 N x (3.0 m / 2)
τ = 75 N*m
So, the student applies a torque of 75 N*m.
To achieve maximum torque, the student would need to apply the force at a 90-degree angle to the radius of the merry-go-round. This is because the sine function (which appears in the formula for torque) is maximized when the angle is 90 degrees.
Therefore, the angle at which the student needs to apply the force to achieve maximum torque is 90 degrees.
If the student continues to push with a force of 50 N, the maximum torque that could be applied would occur when the force is applied at a 90-degree angle to the radius. So, we can use the same formula as before:
2. Torque (τ) = Force (F) x Perpendicular Distance (r)
τ = 50 N x (3.0 m / 2)
τ = 75 N*m
Therefore, the maximum torque that could be applied with a force of 50 N is 75 N*m.
To find the torque applied by the student, we can use the formula:
Torque = Force × Lever Arm × sin(θ)
The force applied by the student is 50 N. The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force. In this case, it is half the diameter of the merry-go-round, which is 1.5 m.
So, the torque applied by the student is:
Torque = 50 N × 1.5 m × sin(110°)
To calculate the angle at which the student should apply the force to achieve maximum torque, we consider that the maximum torque occurs when the force is applied perpendicular to the lever arm. In this case, the lever arm is the radius of the merry-go-round, which is half the diameter, or 1.5 m.
Therefore, the angle to achieve maximum torque is 90°.
Finally, if the student continues to push with a force of 50 N, the maximum torque that could be applied would be when the force is applied perpendicular to the lever arm. In this case, the lever arm is still the radius of the merry-go-round, which is 1.5 m.
So, the maximum torque that could be applied is:
Maximum Torque = 50 N × 1.5 m × sin(90°)
Please note that angles are measured in degrees and it is important to convert them to radians when using trigonometric functions.