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You are pulling a sled with some fire wood on it back to your winter cabin at the top of a snowy hill with a 0 = 30° incline. The combined weight of the sled and wood is 10 lb, and the coefficient of friction between the sled and snow is μ = 0.3. You pull on a rope attached to the sled at an angle of = 20° with respect to the hill surface and accelerates up the hill at i = 2 ft /s² (a) Calculate the tension T in the rope needed to accelerate at this rate. (b) Suppose the sled is 20 ft up the hill, moving at vo = 4 ft/s, when you accidently slip and lets go of the rope. How long does it take for the sled to slide to the base of the hill?

You are pulling a sled with some fire wood on it back to your winter cabin at the top of a snowy hill with a 0 = 30° incline. The combined weight of the sled and wood is 10 lb, and the coefficient of friction between the sled and snow is μ = 0.3. You pull on a rope attached to the sled at an angle of = 20° with respect to the hill surface and accelerates up the hill at i = 2 ft /s² (a) Calculate the tension T in the rope needed to accelerate at this rate. (b) Suppose the sled is 20 ft up the hill, moving at vo = 4 ft/s, when you accidently slip and lets go of the rope. How long does it take for the sled to slide to the base of the hill?

Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter5: The Laws Of Motion
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**Engineering Problem Solving Process: Given, Find, Diagram, Solution.** **Problem Statement:** You are pulling a sled with some firewood on it back to your winter cabin at the top of a snowy hill with a \(\theta = 30^\circ\) incline. The combined weight of the sled and wood is 10 lb, and the coefficient of friction between the sled and snow is \(\mu = 0.3\). You pull on a rope attached to the sled at an angle of \(\phi = 20^\circ\) with respect to the hill surface and accelerate up the hill at \(\ddot{x} = 2 \, \text{ft/s}^2\). (a) Calculate the tension \(T\) in the rope needed to accelerate at this rate. (b) Suppose the sled is 20 ft up the hill, moving at \(v_0 = 4 \, \text{ft/s}\), when you accidentally slip and let go of the rope. How long does it take for the sled to slide to the base of the hill? **Diagram Explanation:** A diagram illustrates the situation: - The hill is inclined at an angle \(\theta\). - The sled is on the incline. - A rope attached to the sled is shown at an angle \(\phi\) with respect to the incline. - The gravitational force \(g\) acts downward. - The frictional force \(\mu\) acts opposite to the direction of motion. - Coordinate axes \(x\) (along the incline) and \(y\) (perpendicular to the incline) are shown for reference.
Transcribed Image Text:**Engineering Problem Solving Process: Given, Find, Diagram, Solution.** **Problem Statement:** You are pulling a sled with some firewood on it back to your winter cabin at the top of a snowy hill with a \(\theta = 30^\circ\) incline. The combined weight of the sled and wood is 10 lb, and the coefficient of friction between the sled and snow is \(\mu = 0.3\). You pull on a rope attached to the sled at an angle of \(\phi = 20^\circ\) with respect to the hill surface and accelerate up the hill at \(\ddot{x} = 2 \, \text{ft/s}^2\). (a) Calculate the tension \(T\) in the rope needed to accelerate at this rate. (b) Suppose the sled is 20 ft up the hill, moving at \(v_0 = 4 \, \text{ft/s}\), when you accidentally slip and let go of the rope. How long does it take for the sled to slide to the base of the hill? **Diagram Explanation:** A diagram illustrates the situation: - The hill is inclined at an angle \(\theta\). - The sled is on the incline. - A rope attached to the sled is shown at an angle \(\phi\) with respect to the incline. - The gravitational force \(g\) acts downward. - The frictional force \(\mu\) acts opposite to the direction of motion. - Coordinate axes \(x\) (along the incline) and \(y\) (perpendicular to the incline) are shown for reference.
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