The document describes calculating the forces and torques acting on a seesaw with a person sitting on one end. It finds that the torque from the person's weight and the torque from the applied force T at the other end are equal, allowing it to calculate T as 300 N. It then sets the horizontal and vertical force components equal to zero to find the force Fp applied by the hinge, determined to be -150 N in the x-direction and 260 N in the y-direction.

1. 54. Adopting the usual convention that torques that would produce counterclockwise rotation are positive,
we have (with axis at the hinge)
L
τz = 0 =⇒ T L sin 60◦ − M g =0
2
where L = 5.0 m and M = 53 kg. Thus, T = 300 N. Now (with Fp for the force of the hinge)
Fx = 0 =⇒ Fpx = −T cos θ = −150 N
Fy = 0 =⇒ Fpy = M g − T sin θ = 260 N
where θ = 60◦ . Therefore (in newtons),
Fp = −150 ˆ + 260 ˆ .
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