Danny and Stacey have gone from the swing to the slide at the park. The slide is inclined at an angle . Danny weighs 39.0 pounds. He is sitting in a cardboard box with a piece of wax paper on the bottom. Stacey is at the top of the slide holding on to the cardboard box. Find the magnitude of the force Stacey must pull with, in order to keep Danny from sliding down the slide. (We are assuming that the wax paper makes the slide into a frictionless surface, so that the only force keeping Danny from sliding is the force with which Stacey pulls.)
A)37.8 lb
B)31.1 lb
C)26.5 lb
D)22.7 lb
E)29.8 lb

Question

Danny and Stacey have gone from the swing to the slide at the park. The slide is inclined at an angle  . Danny weighs 39.0 pounds. He is sitting in a cardboard box with a piece of wax paper on the bottom. Stacey is at the top of the slide holding on to the cardboard box. Find the magnitude of the force Stacey must pull with, in order to keep Danny from sliding down the slide. (We are assuming that the wax paper makes the slide into a frictionless surface, so that the only force keeping Danny from sliding is the force with which Stacey pulls.)​     ​
A)37.8 lb 
B)31.1 lb 
C)26.5 lb 
D)22.7 lb 
E)29.8 lb

Quizplus · Accepted Answer

The force that Stacey must pull with is equal and opposite to the component of gravity parallel to the slide that is acting on Danny. Using trigonometry, we can find that this component is 39.0*sin(11°) = 7.13 pounds. Therefore, Stacey must pull with a force of 7.13 pounds in order to keep Danny from sliding down the slide. Round to the nearest tenth, the answer is 31.1 lb.

Danny and Stacey Have Gone from the Swing to the Slide