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force, Fnet, acting on the vehicle at this time and the angle, 0, between the net force vector and the direction of motion?

force, Fnet, acting on the vehicle at this time and the angle, 0, between the net force vector and the direction of motion?

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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## Scenario A 1530 kg race car is driving around a circular track with a radius of \( r = 104 \) m. In the instant shown in the figure, the vehicle has a forward speed of \( v = 28.9 \) m/s and is slowing down at a rate of \( 4.30 \) m/s². We need to calculate: - The magnitude of the net force, \( F_{\text{net}} \), acting on the vehicle at this time. - The angle, \( \theta \), between the net force vector and the direction of motion. ## Diagram Analysis The image depicts a race car maneuvering along a curved track. The following elements are notable: - **Circular Track**: The track is shown with a radius \( r \), with the car positioned on its circular path. - **Velocity Vector**: An arrow labeled \( v \) indicates the direction of the car's instantaneous velocity. - **Central Force Vector**: An arrow pointing towards the center of the circle indicates the direction of the centripetal force. ## Calculations ### Known Values - Mass, \( m = 1530 \) kg - Radius, \( r = 104 \) m - Speed, \( v = 28.9 \) m/s - Deceleration, \( a = 4.30 \) m/s² ### Net Force, \( F_{\text{net}} \) 1. **Centripetal Force**: \[ F_c = \frac{mv^2}{r} \] 2. **Tangential Force**: \[ F_t = ma \] 3. **Net Force** (combination of radial and tangential forces): \[ F_{\text{net}} = \sqrt{F_c^2 + F_t^2} \] ### Angle, \( \theta \) - Use trigonometric relations to determine the angle: \[ \theta = \tan^{-1}\left(\frac{F_t}{F_c}\right) \] ## Input Fields - \( F_{\text{net}} = \) [Input Box N] (incorrect answer given: \( 2857.5 \) N) - \( \theta = \) [Input Box °] (incorrect answer) This interactive component allows learners to input their
Transcribed Image Text:## Scenario A 1530 kg race car is driving around a circular track with a radius of \( r = 104 \) m. In the instant shown in the figure, the vehicle has a forward speed of \( v = 28.9 \) m/s and is slowing down at a rate of \( 4.30 \) m/s². We need to calculate: - The magnitude of the net force, \( F_{\text{net}} \), acting on the vehicle at this time. - The angle, \( \theta \), between the net force vector and the direction of motion. ## Diagram Analysis The image depicts a race car maneuvering along a curved track. The following elements are notable: - **Circular Track**: The track is shown with a radius \( r \), with the car positioned on its circular path. - **Velocity Vector**: An arrow labeled \( v \) indicates the direction of the car's instantaneous velocity. - **Central Force Vector**: An arrow pointing towards the center of the circle indicates the direction of the centripetal force. ## Calculations ### Known Values - Mass, \( m = 1530 \) kg - Radius, \( r = 104 \) m - Speed, \( v = 28.9 \) m/s - Deceleration, \( a = 4.30 \) m/s² ### Net Force, \( F_{\text{net}} \) 1. **Centripetal Force**: \[ F_c = \frac{mv^2}{r} \] 2. **Tangential Force**: \[ F_t = ma \] 3. **Net Force** (combination of radial and tangential forces): \[ F_{\text{net}} = \sqrt{F_c^2 + F_t^2} \] ### Angle, \( \theta \) - Use trigonometric relations to determine the angle: \[ \theta = \tan^{-1}\left(\frac{F_t}{F_c}\right) \] ## Input Fields - \( F_{\text{net}} = \) [Input Box N] (incorrect answer given: \( 2857.5 \) N) - \( \theta = \) [Input Box °] (incorrect answer) This interactive component allows learners to input their
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