A book sits on a horizontal top of a car as the car accelerates horizontally from rest.If the coefficient static of friction between the book and the car top is 0.450,what is the maximum acceleration the car can have if the book is not to slip?
I remember when as a Electrical Engineering student at the University of Texas, one morning I looked in my mirror and saw my books and papers behind in the street. I forgot to put them in when unlocking the car. So goes all night studying.
The weight of the books is mg, so the maximum force of friction is mg*mu.
This is equal to m*acceleration.
set them equal, and solve for acceleration. Notice mass m divides out.
To find the maximum acceleration the car can have without the book slipping, we can use the equation:
Maximum force of friction = m * acceleration
The maximum force of friction can be calculated using the formula:
Maximum force of friction = coefficient of static friction * weight of the book
Given that the coefficient of static friction between the book and the car top is 0.450, we can substitute this value in the equation:
Maximum force of friction = 0.450 * weight of the book
Since the weight of the book is given by the formula:
Weight of the book = m * g
where m is the mass of the book and g is the acceleration due to gravity (approximately 9.8 m/s^2), we can substitute this value in the equation:
Weight of the book = m * 9.8
Substituting the value of the weight of the book in the equation for the maximum force of friction, we have:
Maximum force of friction = 0.450 * (m * 9.8)
Now, we set the maximum force of friction equal to m times the acceleration:
0.450 * (m * 9.8) = m * acceleration
Simplifying the equation by cancelling out the mass m, we get:
0.450 * 9.8 = acceleration
Finally, we calculate the maximum acceleration:
acceleration = 0.450 * 9.8
Therefore, the maximum acceleration the car can have without the book slipping is approximately 4.41 m/s^2.
To solve this problem, you need to use the concept of static friction and Newton's second law of motion.
First, let's break down the information provided:
- The coefficient of static friction between the book and the car top is given as 0.450.
- The weight of the book is given as mg, where m is the mass of the book, and g is the acceleration due to gravity.
- The maximum force of friction is equal to mg * μ (where μ is the coefficient of static friction).
- The maximum force of friction acting on the book is equal to m * acceleration (where acceleration is the acceleration of the car).
Now, let's set up the equation:
mg * μ = m * acceleration
Since the mass (m) cancels out on both sides of the equation, we can simplify it to:
g * μ = acceleration
Finally, we substitute the given value of the coefficient of static friction (μ = 0.450) into the equation and solve for acceleration:
acceleration = g * 0.450
Acceleration is the maximum value the car can have without the book slipping.