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Problem 1 Cat Lift 2mg Three ropes are attached to the center of a box that has mass m and is being lifted up. The magnitude of the tension in each rope is shown. (a) How much work do the ropes do over a vertical distance h? (b) How much work does gravity do over the same distance? (c) If the box initially had zero speed, what is the speed at the distance h? 45% mg 30° 2mg

Problem 1 Cat Lift 2mg Three ropes are attached to the center of a box that has mass m and is being lifted up. The magnitude of the tension in each rope is shown. (a) How much work do the ropes do over a vertical distance h? (b) How much work does gravity do over the same distance? (c) If the box initially had zero speed, what is the speed at the distance h? 45% mg 30° 2mg

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem 1: Cat Lift** Three ropes are attached to the center of a box that has mass \( m \) and is being lifted up. The magnitude of the tension in each rope is shown. (a) How much work do the ropes do over a vertical distance \( h \)? (b) How much work does gravity do over the same distance? (c) If the box initially had zero speed, what is the speed at the distance \( h \)? --- **Diagram Explanation:** The diagram illustrates a box with a cat on top being lifted by three ropes. The forces and angles for each rope are indicated as follows: - The top left rope exerts a force of \(2mg\) at an angle of 45 degrees from the horizontal. - The top right rope exerts a force of \(\frac{\sqrt{2}}{2}mg\) at an angle of 30 degrees from the horizontal. - The bottom rope exerts a force of \(\frac{1}{2}mg\) vertically downward, representing the gravitational force acting on the box.
Transcribed Image Text:**Problem 1: Cat Lift** Three ropes are attached to the center of a box that has mass \( m \) and is being lifted up. The magnitude of the tension in each rope is shown. (a) How much work do the ropes do over a vertical distance \( h \)? (b) How much work does gravity do over the same distance? (c) If the box initially had zero speed, what is the speed at the distance \( h \)? --- **Diagram Explanation:** The diagram illustrates a box with a cat on top being lifted by three ropes. The forces and angles for each rope are indicated as follows: - The top left rope exerts a force of \(2mg\) at an angle of 45 degrees from the horizontal. - The top right rope exerts a force of \(\frac{\sqrt{2}}{2}mg\) at an angle of 30 degrees from the horizontal. - The bottom rope exerts a force of \(\frac{1}{2}mg\) vertically downward, representing the gravitational force acting on the box.
Expert Solution
Step 1

The weight of the box will always act in the downward direction.

a)

Calculate the vertical component of the force.

FV=[(2mg)sin45°+(22mg)sin30°−(12mg)]−mgFV=0.27mg

Calculate the work done by the ropes to cover the vertical distance h.

W=FV×hW=0.27mgh

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