How to Analyze the FBD of a Toy Car on the Underside of a Dome?

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In summary, to analyze the Free Body Diagram (FBD) of a toy car on the underside of a dome, first identify all the forces acting on the toy car, including gravitational force, normal force, and any frictional forces. Next, represent these forces in a diagram, ensuring to indicate their directions and magnitudes. Use the geometry of the dome to understand how the curved surface affects the orientation of the forces. Finally, apply Newton's laws of motion to analyze the equilibrium or motion of the toy car, ensuring to account for the dome's curvature in your calculations.
  • #1
bobbeh
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Homework Statement
Draw the FBD including Kinetic Friction, Gravity, and Normal force
Relevant Equations
Fnet = mv^2/r
weight pointing down
Fn pointing down and to the left (to the center of the dome)
Fs pointing ..?? Should it not be off the page? Maybe up and off the page to oppose movement + gravity?
 
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  • #2
bobbeh said:
Homework Statement: Draw the FBD including Kinetic Friction, Gravity, and Normal force
Relevant Equations: Fnet = mv^2/r

weight pointing down
Fn pointing down and to the left (to the center of the dome)
Fs pointing ..?? Should it not be off the page? Maybe up and off the page to oppose movement + gravity?
Can you post a labeled diagram of your "vertically horizontal circle on the underside of a dorm" please?
 
  • #3
Hi @bobbeh and welcome to PF.

The title:
"FBD of a toy car moving in a vertically horizontal circle on the underside of a dome"
is not clear.

Is the plane in which the circle lies horizontal or vertical (or something else)?
Is the car'speed constant?
Are the car's wheel rolling without slipping?
At what position is the car on the dome?

You need to provide the complete and exact original question, word-for-word (and as already noted by @renormalize, a diagram).
 
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FAQ: How to Analyze the FBD of a Toy Car on the Underside of a Dome?

What is an FBD (Free Body Diagram) and why is it important for analyzing the motion of a toy car in a vertically horizontal circle?

An FBD, or Free Body Diagram, is a graphical representation used to visualize the forces acting on an object. It is important for analyzing the motion of a toy car in a vertically horizontal circle because it helps identify and quantify the different forces at play, such as gravitational force, normal force, and centripetal force, which are crucial for understanding the car's motion and stability.

What forces act on the toy car as it moves in a vertically horizontal circle on the underside of a dome?

The primary forces acting on the toy car are the gravitational force (weight) acting downward, the normal force exerted by the surface of the dome acting perpendicular to the surface, and the centripetal force required to keep the car moving in a circular path. The centripetal force is provided by the component of the normal force and possibly friction if the surface is not frictionless.

How do you determine the direction of the normal force in the FBD of the toy car?

The normal force is always directed perpendicular to the surface of contact. For a toy car moving on the underside of a dome, the normal force will be directed radially inward towards the center of the dome. This inward direction is necessary to provide the centripetal force required for circular motion.

How does the speed of the toy car affect the forces in the FBD?

The speed of the toy car affects the magnitude of the centripetal force required to maintain circular motion. As the speed increases, the centripetal force, which is given by the equation \( F_c = \frac{mv^2}{r} \) (where \( m \) is the mass of the car, \( v \) is its velocity, and \( r \) is the radius of the circular path), also increases. This means that the normal force must increase to provide the necessary centripetal force, assuming the radius remains constant.

What role does friction play in the motion of the toy car in a vertically horizontal circle?

Friction can play a significant role in maintaining the motion of the toy car. If the surface of the dome is not frictionless, frictional force can provide additional centripetal force to help keep the car in its circular path. Additionally, friction can prevent the car from slipping off the surface of the dome. The direction of the frictional force would be tangential to the circle and opposite to the direction of any relative motion between the car and the dome's surface.

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