Unlike its value on a horizontal surface, n is less than the weight of the sled

Question

Unlike its value on a horizontal surface, n is less than the weight of the sled when the sled is on the slope. This is because only part of the force of gravity (the x - component) is acting to pull the sled down the slope. The y - component of the force of gravity balances the normal force. Consider the same scenario on a hill with a steeper slope. Which quantity or quantities would increase? (Select all that apply.) mg cos theta mg sin theta The tension. The angle theta The magnitude n of the normal force. 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 70.0 N, find the force exerted by the rope on the sled and the magnitude of the force n_s exerted by the hill on the sled. Force exerted by the rope on the sled N Force exerted by the hill on the sled 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 61.5 N, find the weight of the child and the magnitude of the normal force acting on the sled. weight of the child N Normal force on the sled N

Explanation / Answer

a) if slope changes mg sintheta and mg costheta , angle , tension and normal force changes

practice: T = mgsintheta = 70*sin30 = 35 N

N = mgcos30 = 60.6 N

exercise:

T = (mg+w)sin30

N = (mg+w)cos30

mg+w = T/sin30 = 61.5*2 = 123 N

N = 123*cos30 = 106.52 N

w = 123-70 = 53 N

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