A contestant in a winter sporting event pulls an m kg block of ice across a frozen lake by applying a force F at an angle θ above the horizontal as shown. Assume that the coefficient of static friction for ice on ice is 0.0300, and the coefficient of kinetic friction for the same is 0.0100. Let to the right be the positive x direction and up be the positive y direction for your equations. Obtain a numeric value, in newtons, for the magnitude of the maximum applied force, F, consistent with static friction when the force makes an angle 22° above the horizontal and the mass of the block is 34 kg.  Obtain a numeric value for the acceleration, a, in meters per squared seconds, when the mass of the block is 34 kg and the angle of the rope is 22° above the horizontal.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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A contestant in a winter sporting event pulls an m kg block of ice across a frozen lake by applying a force F at an angle θ above the horizontal as shown. Assume that the coefficient of static friction for ice on ice is 0.0300, and the coefficient of kinetic friction for the same is 0.0100. Let to the right be the positive x direction and up be the positive y direction for your equations.

Obtain a numeric value, in newtons, for the magnitude of the maximum applied force, F, consistent with static friction when the force makes an angle 22° above the horizontal and the mass of the block is 34 kg. 

Obtain a numeric value for the acceleration, a, in meters per squared seconds, when the mass of the block is 34 kg and the angle of the rope is 22° above the horizontal. 

 

The image illustrates a person pulling a block of ice across a surface. The person is wearing winter clothing and is leaning forward, with a rope extending from their hands to the block of ice.

Key elements of the diagram:

1. **Force Vector (F):** An arrow represents the force applied by the person. The arrow is angled upwards, indicating that the force has both vertical and horizontal components.

2. **Angle (θ):** The angle between the horizontal surface and the direction of the applied force (F) is labeled as θ (theta). This angle is crucial in understanding how the force is split into components.

3. **Rope:** A rope connects the person to the ice block, illustrating the method of force application.

This diagram can be used to explain concepts such as force decomposition, where the applied force is divided into horizontal and vertical components. It also demonstrates practical applications of physics concepts like friction and tension.
Transcribed Image Text:The image illustrates a person pulling a block of ice across a surface. The person is wearing winter clothing and is leaning forward, with a rope extending from their hands to the block of ice. Key elements of the diagram: 1. **Force Vector (F):** An arrow represents the force applied by the person. The arrow is angled upwards, indicating that the force has both vertical and horizontal components. 2. **Angle (θ):** The angle between the horizontal surface and the direction of the applied force (F) is labeled as θ (theta). This angle is crucial in understanding how the force is split into components. 3. **Rope:** A rope connects the person to the ice block, illustrating the method of force application. This diagram can be used to explain concepts such as force decomposition, where the applied force is divided into horizontal and vertical components. It also demonstrates practical applications of physics concepts like friction and tension.
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