A car can decelerate at -4.40 m/s2 without skidding when coming to rest on a level road. What would be the magnitude of its deceleration if the road were inclined at 12° uphill? Assume the same static friction coefficient.
The friction force on the tires remains -4.40 m/s^2*M if tires are on the verge of slipping. Gravity will apply an additional retarding force of -M g sin 12 = 2.04 m/s^2*M
The resultant deceleration is
(-4.40 - 2.04) M/M
= -6.44 m/s^2
(mass M cancels out)
To find the magnitude of the car's deceleration on an inclined road, we need to consider the forces acting on the car.
When the car is on a level road, the forces acting on it are the force of static friction, opposing the car's motion, and the gravitational force acting downward. These forces balance each other, resulting in the car's deceleration.
However, when the road is inclined uphill, the force of gravity acts at an angle relative to the road. We need to break down the gravitational force into its components parallel and perpendicular to the road.
1. Find the gravitational force component parallel to the road:
F_parallel = m * g * sin(θ), where m is the mass of the car, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the road inclination (12°).
2. The static friction force should oppose the component of gravity, which is trying to pull the car downhill. Therefore, the magnitude of the static friction force remains the same as before, which is equal to the car's mass times the acceleration on a level road: F_friction = m * a.
3. Since the car is coming to rest, the net force acting on the car is the difference between the static friction force and the component of gravity.
Net Force = F_friction - F_parallel
4. Finally, we can find the deceleration on the inclined road.
a_new = Net Force / m
Now let's plug in the given values:
θ = 12°
a = -4.40 m/s^2
1. Calculate F_parallel:
F_parallel = m * g * sin(θ) = m * 9.8 m/s^2 * sin(12°)
2. Since the static friction force F_friction equals m * a (from the given information), we can directly use it in the equations.
3. Calculate the net force:
Net Force = F_friction - F_parallel
4. Calculate the deceleration on the inclined road:
a_new = Net Force / m
Plugging in the values and performing the calculations will give the magnitude of the car's deceleration on the inclined road.