A 14.5-m uniform ladder weighing 485 N rests against a frictionless wall. The ladder makes a 63.0 angle with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 805-N firefighter has climbed 3.84 m along the ladder from the bottom. (b) If the ladder is just on the verge of slipping when the firefighter is 9.35 m from the bottom, what is the coefficient of static friction between ladder and ground? Part 1 of 4 - Conceptualize Refer to the force diagram in the figure. Since the wall is frictionless, only the ground exerts an upward force on the ladder to oppose the combined weight of the ladder and firefighter, son. = mig + m29. Based on the angle of the ladder, we expect that the force of static friction is less than the sum of the weights of the ladder and the firefighter. We estimate the coefficient of friction to be somewhere between 0 and 1. m2g nw 9 Vmig O Part 2 of 4 - Categorize Using the force diagram, apply Newton's second law, and sum the torques to find the unknown forces. Since this is a static problem (no motion), both the net force and the net torque are zero. Part 3 of 4 - Analyze (a) The wall is frictionless, but it does exert a horizontal normal force 7,. For the x and y components of the force, we have the following from Newton's second law. Ex = f - nw = 0 N - 485 N = 0 Taking torques about an axis at the foot of the ladder, we have the following. Er = 0 IN) (3.84 m ) sin 276 + (485 N) m sin 270 -nw m) cos 279 Solving this equation for n , we have (3.84 m) N ) + m) (485 NV)| tan 270 n wm)A carpenter's square has the shape of an L as shown in the figure below. Locate its center of gravity. (Take (x, y) = (0, 0) at the intersection of d, and d. Assumed, = 17.0 cm, d, = 3.00 cm, d, = 3.00 cm, and d = 15.0 cm.) cm d2 da A Need Help? Read It Watch ItYour brother is opening a skateboard shop. He has created a sign for his shop made from a uniform material and in the shape shown in the figure. 1.00 m 5.00 cm 3.00 m A The shape of the sign represents one of the hills in the skateboard park he plans on building on land adjacent to the shop. The curve on the top of the sign is described by the function y = (X - 3)". When the sign arrives in his shop, your brother wants to hang it from a single wire outside the shop. But 9 he doesn't know where on the sign to attach the wire so that the bottom edge of the sign will hang in a horizontal orientation. He asks for your help. (Enter the x-component in m.) m Need Help? Read It