A 1500 kg car moves along a horizontal road
at speed v0 = 21.9 m/s. The road is wet,
so the static friction coefficient between the
tires and the road is only µs = 0.302 and
the kinetic friction coefficient is even lower,
µk = 0.2114.
The acceleration of gravity is 9.8 m/s^2
Assume: No aerodynamic forces; g =
9.8 m/s^2
Forward is the positive direction.
What is the highest possible deceleration of
the car under such conditions?
Answer in units of m/s^2
2.96
12
To find the highest possible deceleration of the car, we need to determine the maximum friction force that can be exerted on the car by the road.
The maximum static friction force (F_static_max) can be calculated using the formula:
F_static_max = µ_s * N
where µ_s is the static friction coefficient and N is the normal force.
The normal force (N) is equal to the weight of the car, which can be calculated using:
N = m * g
where m is the mass of the car and g is the acceleration due to gravity.
Plugging in the values given, we have:
m = 1500 kg
g = 9.8 m/s^2
N = (1500 kg) * (9.8 m/s^2)
N = 14700 N
Now we can calculate the maximum static friction force:
F_static_max = (0.302) * (14700 N)
F_static_max = 4439.4 N
The maximum static friction force is the maximum force that can be exerted to prevent the car from sliding.
Since the question asks for the highest possible deceleration, we assume that the deceleration is caused by kinetic friction. The kinetic friction force (F_kinetic) can be calculated using the formula:
F_kinetic = µ_k * N
where µ_k is the kinetic friction coefficient.
Using the given values:
µ_k = 0.2114
N = 14700 N
F_kinetic = (0.2114) * (14700 N)
F_kinetic = 3104.958 N
The highest possible deceleration of the car can be calculated using Newton's second law of motion:
F = m * a
where F is the force and m is the mass of the car.
Rearranging the equation to solve for acceleration:
a = F / m
Plugging in the values:
F = F_kinetic = 3104.958 N
m = 1500 kg
a = (3104.958 N) / (1500 kg)
Calculating the highest possible deceleration:
a ≈ 2.07 m/s^2
Therefore, the highest possible deceleration of the car under these conditions is approximately 2.07 m/s^2.