Not sure how to draw the diagram to this, or quite how to solve b and c: 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.

a. What torque does the student apply? (I think the answer is 141, assuming I used the correct angle, not sure because I can't draw the diagram).
b. What angle would the student need to apply the force to achieve maximum torque?
c. If the student continues to push with a force of 50 N, what maximum torque could be applied?

THANKS!

How did you get 90? I get 70, isn't it 180-110? Oh, my mistake, there was a diagram with an arrow and the arrow as going at an angle of 110 degrees. Sorry!

With the information you have given:

A. 150 Nm assuming that the angle that student pushes is 90 degrees to the merry-go-round.
if the angle is not 90 degrees then the force = 50 N * sin(theta)
b.90 degrees

I am struggling with the same problem can you send me the answers.

To solve this problem, you can use the formula for torque:

Torque = Force * Distance * sin(θ)

where torque is measured in Newton-meters (Nm), force is measured in Newtons (N), distance is the perpendicular distance from the point of rotation to the line of action of the force, and θ is the angle between the force vector and the line connecting the point of rotation to the point of application of the force.

a. To find the torque, you will first need to calculate the distance. Since the diameter of the merry-go-round is given as 3.0 m, the radius (distance from the center to the edge) would be half of that, which is 1.5 m.

Torque = 50 N * 1.5 m * sin(θ)

Now, you mentioned that you used an angle to calculate a torque of 141 Nm. Without the diagram, it would be challenging to determine if the angle you used is correct or not. However, assuming you are using the correct angle, your answer seems to be correct.

b. To achieve maximum torque, the force should be applied perpendicular (at 90 degrees) to the line connecting the point of rotation to the point of application of force. This means that the angle (θ) would be 90 degrees.

c. If the student continues to push with a force of 50 N, the maximum torque that could be applied would be achieved when the force is applied perpendicular to the line connecting the point of rotation to the point of application of force (θ = 90 degrees). So, using the same calculations as in part a:

Torque = 50 N * 1.5 m * sin(90°) = 50 N * 1.5 m * 1 = 75 Nm

Therefore, if the student continues to push with a force of 50 N, the maximum torque achievable would be 75 Nm.