Final answer:
The maximum speed at which an automobile can move around an unbanked curve with a coefficient of friction of 0.8 and a radius of 84.5 meters is 26 m/s. This computation is based on the relationship between centripetal force and friction, using the formula v = √(μrg).
Step-by-step explanation:
To determine the maximum speed at which an automobile can move around a curve without slipping, we use the equation for centripetal force, ∑F = mac, where mac is the centripetal force necessary to keep the car moving in a circle and ∑F is the sum of forces acting upon the car, in this case, the frictional force. To find the maximum speed, we can set the frictional force (which has an upper limit due to the coefficient of friction, μ, and the normal force, N) equal to the centripetal force needed. Since the normal force is equal to the weight of the car (mg), and the frictional force is μN, we have μmg=mv2/r.
Cancelling out the shared terms and solving for v gives us v = √(μrg). Plugging in the values (μ = 0.8, r = 84.5 m, and g = 10 m/s2), we get a maximum speed v = √(0.8*84.5*10) m/s, which simplifies to v = √(676) m/s, resulting in v = 26 m/s.
The correct answer to the student's question is A. 26 ms-1.