A sports car with a very powerful engine driving on a surface with a coefficient of static
friction µs = 0.8 wants to accelerate from a stop to 100 km/hr. (You may neglect air
resistance.)
a) What is the fastest that the car can accomplish this?
b) How far will the car travel in this time?
c) Suppose that the mass of the car is 1500 kg. What is the maximum power output required
from the engine in order to accomplish this?
change 100km/hr to m/s
vf=at=Force/mass * t
vf=mu*mg/m *t=mu*g*t
solve for t
b. d=1/2 a t^2
c. power=energy/time
= (force*distance)/time=mu*mg*d/time
now notice d/time is avg velocity=vf/2
This all ignores rolling friction, or kinetic
Thank you! Would you know how do this question if it was going up a 10 degree incline?
To answer these questions, we can use the principles of Newton's laws of motion. Let's break it down step by step:
a) To determine the fastest acceleration, we need to consider the maximum frictional force available for the car to achieve this acceleration. The maximum frictional force can be calculated using the equation:
F_friction = µs * normal force
In this case, the normal force is equal to the weight of the car, which can be calculated as the mass of the car multiplied by the acceleration due to gravity (9.8 m/s²).
normal force = mass * acceleration due to gravity
So, the maximum frictional force can be calculated as:
F_friction = µs * (mass * acceleration due to gravity)
Once we have the maximum frictional force, we can calculate the maximum acceleration using Newton's second law:
F_net = mass * acceleration
Since the car is starting from rest and we want to know the maximum acceleration, the net force on the car is the maximum frictional force. Hence, we have:
maximum acceleration = F_friction / mass
Finally, we can calculate the time it takes for the car to reach the desired speed using the following equation of motion:
v = u + a*t
Where:
v = final velocity (100 km/hr or 27.8 m/s)
u = initial velocity (0 m/s)
a = maximum acceleration
t = time taken
Rearranging the equation, we get:
t = (v - u) / a
b) To calculate the distance travelled by the car, we can use the equation of motion that relates initial velocity, final velocity, acceleration, and distance:
s = (u * t) + (0.5 * a * t^2)
Where:
s = distance travelled
c) To calculate the maximum power output required from the engine, we can use the equation:
Power = (Force * distance) / time
In this case, the force can be calculated as the product of mass and acceleration, distance is the result from part b), and time is the result from part a).
Note: Make sure to convert units to be consistent (e.g. converting km/hr to m/s).
By plugging in the values and solving these equations step by step, you can find the answers to each question.