While Driving Around A Curve Of 200 M Radius, You Notice That The fuzzy dice Hanging From The Rear-view Mirror Hangs At An Angle Of 15 Degree To The Vertical. 1.) What is the force diagram for the dice?
2.) What are the equations of motion in the horizontal and vertical directions (apply Newton's Law of motion)
3.) What should the speedometer of your car read kilometers per hour?
on the dice, gravity down, and horizontal centripetal force.
Tan15=v^2/gr
solve for v.
1.) To determine the force diagram for the dice, we need to consider the forces acting on it. In this case, the only force acting on the dice is the force of gravity pulling it downwards. The force diagram would therefore consist of a downward force (mg), where m is the mass of the dice and g is the acceleration due to gravity.
2.) Based on Newton's law of motion, we can write the equations of motion for the dice in both the horizontal and vertical directions.
In the horizontal direction, there is no net force acting on the dice since it is moving in a circular path. Therefore, the equation of motion is:
F(horizontal) = ma(horizontal)
0 = ma(horizontal)
In the vertical direction, the force of gravity is acting on the dice. This force can be broken down into two components: the component perpendicular to the curve (mgcosθ) and the component tangential to the curve (mgsinθ). The equation of motion in the vertical direction becomes:
F(vertical) = ma(vertical)
mgcosθ = ma(vertical)
3.) To determine the car's speedometer reading in kilometers per hour, we need to use the centripetal force equation:
F = mv²/r
In this case, the centripetal force is equal to the force of gravity component tangential to the curve (mgsinθ). Rearranging the equation, we get:
mgsinθ = mv²/r
We can solve for v to find the car's speed:
v = sqrt((r * g * sinθ) / m)
We know the radius of the curve (200 m) and the angle θ (15 degrees), so we can substitute these values into the equation to find the speed in meters per second (m/s). To convert this to kilometers per hour, simply multiply by 3.6.
Note: Make sure to convert the angle θ from degrees to radians before substituting it into the equation. 1 degree = π/180 radians.