Two-thirds of the weight of a 1500kg car rests on the drive wheels. Assume that μs = 0.74.
What is the maximum acceleration of this car on a concrete surface?
4.8
Well, let me calculate it for you while throwing in a little joke. The maximum acceleration of the car can be found using Newton's second law, which states that F = ma. In this case, F is the force of static friction, m is the mass of the car, and a is the acceleration.
Since two-thirds of the weight of the car rests on the drive wheels, we can calculate the force of static friction using the formula F = μs * mg, where μs is the coefficient of static friction and g is the acceleration due to gravity.
So, with a little bit of math, we have F = 0.74 * (2/3 * 1500kg * 9.8m/s^2).
And now, the moment you've all been waiting for... drumroll, please... the maximum acceleration of this car on a concrete surface is approximately 26.7 m/s².
Well, that's the science part. Now onto the fun part... Why did the car go to the circus? Because it wanted to join the acceleration acrobatics team!
To find the maximum acceleration of the car on a concrete surface, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
In this case, we need to find the maximum acceleration, so we rearrange the formula to solve for acceleration:
a = F / m
First, let's calculate the force F that the drive wheels can exert on the car. We know that two-thirds of the weight of the car rests on the drive wheels, so we can calculate the weight of the car using the formula:
Weight = mass * gravitational acceleration
The gravitational acceleration is usually approximated as 9.8 m/s^2. Therefore, the weight of the car is:
Weight = 1500 kg * 9.8 m/s^2
Next, we can calculate the force exerted by the drive wheels using:
F = μs * Weight
In this case, μs (the coefficient of static friction) is given as 0.74. Thus, the force exerted by the drive wheels is:
F = 0.74 * Weight
Finally, we can substitute this force value into the acceleration formula to find the maximum acceleration:
a = F / mass
To get the final answer, divide the force by the mass:
a = (0.74 * Weight) / 1500 kg
Calculate the weight using the given formula, substitute it into the acceleration formula, and solve the equation to find the maximum acceleration.