In a homework problem you encounter the following problem: "A car of mass m=2100 kg travels at a constant speed v=90 km/hr when it is at the bottom of a dip in the road, as shown in the diagram below. The dip in the road is circular with radius r=25 m. What is the magnitude of the normal force of that the road exerts on the car?" Which free body diagram below best represents the forces on the car? Note that the length of each vector is proportional to its magnitude FN E FN Fmotion mg mg Fcentrifugal FN Fmotion FN mg Fcentrifugal mg -------

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Chapter1: Units, Trigonometry. And Vectors
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In a homework problem, you encounter the following scenario:

"A car of mass \( m = 2100 \, \text{kg} \) travels at a constant speed \( v = 90 \, \text{km/hr} \) when it is at the bottom of a dip in the road, as shown in the diagram below. The dip in the road is circular with radius \( r = 25 \, \text{m} \). What is the magnitude of the normal force that the road exerts on the car?"

**Diagram:**
The image shows a side view of a car at the bottom of a circular dip in the road. The car is positioned at the lowest point of the dip, and the path of the road is represented by a curved line. The radius, \( r \), and velocity, \( v \), are indicated with arrows.

**Free Body Diagrams:**

The image presents three possible free body diagrams that represent the forces acting on the car:

1. **Option 1:**
   - \( F_N \) (Normal Force) is pointing upwards.
   - \( mg \) (Gravitational Force) is pointing downwards.
   - \( F_{\text{centrifugal}} \) is pointing downwards.
   - The total length of the vectors represents their relative magnitudes.

2. **Option 2:**
   - \( F_N \) (Normal Force) is pointing upwards.
   - \( F_{\text{motion}} \) is pointing to the right.
   - \( mg \) (Gravitational Force) is pointing downwards.
   - The vectors’ lengths are proportional to the force magnitudes. This option lacks the \( F_{\text{centrifugal}} \) force.

3. **Option 3:**
   - \( F_N \) (Normal Force) is pointing upwards.
   - \( F_{\text{motion}} \) is pointing to the right.
   - \( mg \) (Gravitational Force) is pointing downwards.
   - \( F_{\text{centrifugal}} \) is pointing downwards.
   - The vectors’ lengths are proportional to the force magnitudes.

The question asks which free body diagram best represents the forces on the car, with the note that the length of each vector is proportional to its magnitude.
Transcribed Image Text:In a homework problem, you encounter the following scenario: "A car of mass \( m = 2100 \, \text{kg} \) travels at a constant speed \( v = 90 \, \text{km/hr} \) when it is at the bottom of a dip in the road, as shown in the diagram below. The dip in the road is circular with radius \( r = 25 \, \text{m} \). What is the magnitude of the normal force that the road exerts on the car?" **Diagram:** The image shows a side view of a car at the bottom of a circular dip in the road. The car is positioned at the lowest point of the dip, and the path of the road is represented by a curved line. The radius, \( r \), and velocity, \( v \), are indicated with arrows. **Free Body Diagrams:** The image presents three possible free body diagrams that represent the forces acting on the car: 1. **Option 1:** - \( F_N \) (Normal Force) is pointing upwards. - \( mg \) (Gravitational Force) is pointing downwards. - \( F_{\text{centrifugal}} \) is pointing downwards. - The total length of the vectors represents their relative magnitudes. 2. **Option 2:** - \( F_N \) (Normal Force) is pointing upwards. - \( F_{\text{motion}} \) is pointing to the right. - \( mg \) (Gravitational Force) is pointing downwards. - The vectors’ lengths are proportional to the force magnitudes. This option lacks the \( F_{\text{centrifugal}} \) force. 3. **Option 3:** - \( F_N \) (Normal Force) is pointing upwards. - \( F_{\text{motion}} \) is pointing to the right. - \( mg \) (Gravitational Force) is pointing downwards. - \( F_{\text{centrifugal}} \) is pointing downwards. - The vectors’ lengths are proportional to the force magnitudes. The question asks which free body diagram best represents the forces on the car, with the note that the length of each vector is proportional to its magnitude.
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