Calculate the maximum acceleration of a car that is heading up a 9.5° slope, assume that only half the weight of the car is supported by the two drive wheels and that the static coefficient of friction is 1.
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To calculate the maximum acceleration of a car on a slope, we need to consider the forces acting on the car. In this case, we have the gravitational force pulling the car down the slope and the frictional force between the tires and the road that opposes this motion.
First, we need to determine the gravitational force acting on the car. We can calculate this using the formula:
F_gravity = m * g
Where:
- F_gravity is the gravitational force
- m is the mass of the car
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Next, we need to calculate the normal force, which is the force that the road exerts on the car perpendicular to the slope. Since only half the weight of the car is supported by the two drive wheels, we can calculate the normal force as:
N = (m * g) / 2
The frictional force can be determined using the formula:
F_friction = μ * N
Where:
- F_friction is the frictional force
- μ is the coefficient of friction
- N is the normal force
Given that the static coefficient of friction is 1, we substitute this value into the equation:
F_friction = 1 * N
Now, we can calculate the maximum acceleration:
a = (F_friction) / (m)
Substituting the values we have:
a = (N) / (2m)
To find the maximum acceleration, we need to convert the slope angle from degrees to radians:
θ = 9.5° * (π/180)
Finally, we can substitute the values into the equation to calculate the maximum acceleration.