94% Fri 10:52 AM a Screen Shot 2020-02-07 at 10.26.30 AM Q Search EXAMPLE 4.6 Sled on a Frictionless Hill Goal Use the second law and the normal force in an equilibrium problem. Problem A sled is tied to a tree on a frictionless, snow-covered hill, as shown in figure (a). If the sled weighs 77.0 N, find the force exerted by the rope on the sled and the mg sin e 30.00 magnitude of the force ñ exerted by the hill on mg cos e the sled. F = mig %3D 80.0° Strategy When an object is on a slope, it's convenient to use tilted coordinates, as in figure (b), so that the normal force n is in the y-direction and the tension force T is in the x- (a) (b) (a) A sled tied to a tree on a frictionless hill. (b) A free- body diagram for the sled. direction. In the absence of friction, the hill exerts no force on the sled in the x-direction. Because the sled is at rest, the conditions for equilibrium, EFx 0 and Σ, 0 apply, giving two equations for the two unknowns--the tension and the normal %3D %3D force. SOLUTION EF = † + fñ + F¸ = 0 Apply Newton's second law to the sled, with a = 0. %3D EF, = T + 0 - mg sin0 =T - (77.0 N)(sin 30.0°) = 0 Extract the x-component from this %3D equation to find T. The x-component of T = 38.5 N the normal force is zero, and the sled's weight is given by mg = 77.0 N. %3D = 0 + n - mg cos® =n - (77.0 N)(cos 30.0°) = 0 Write the y-component of Newton's second law. The y-component of the n = 66.7 N tension is zero, so this equation will give the normal force. Window Help Tools Go View Edit File Preview a Screen Shot 2020-02-07 at 3.43.03 AM Q Search Question Consider the same scenario on a hill with a steeper slope. Which quantity or quantities would increase? (Select all that apply.) O The angle 0. mgsine The tension. mg cos0 The magnitude n of the normal force. PRACTICE IT Use the worked example above to help you solve this problem. A sled is tied to a tree on a frictionless, snow-covered hill, as shown in Figure (a). If the sled weighs 79.0 N, find the force exerted by the rope on the sled and the magnitude of the force ns exerted by the hill on the sled. Force exerted by the rope on the sled Force exerted by the hill on the sled GETTING STARTED I I'M STUCK! HINTS: EXERCISE Use the values from PRACTICE IT to help you work this exercise. Suppose a child of weight w climbs onto the sled. If the tension force is measured to be 61.0 N, find the weight of the child and the magnitude of the normal force acting on the sled. Weight of the child Normal force on the sled N.