A glass of orange juice is on the floor of a subway car traveling along a straight path at constant velocity. Everything's fine. The coefficient of static friction between the glass and the floor is 0.32. The subway suddenly accelerates forward. What is the maximum acceleration that the subway car can have without the orange juice sliding backward on the floor.
To find the maximum acceleration that the subway car can have without the orange juice sliding backward on the floor, we need to determine the force of friction between the glass and the floor.
The force of friction can be calculated using the equation:
F_friction = coefficient of friction * normal force
In this case, the normal force is equal to the weight of the glass, which can be calculated using the equation:
normal force = mass * gravitational acceleration
Assuming we have the mass of the glass, we need to know the value of the gravitational acceleration. On Earth, close to the surface, the standard value for gravitational acceleration is approximately 9.8 m/s^2.
Once we calculate the force of friction, we can equate it to the product of mass and acceleration to find the maximum acceleration without the orange juice sliding backward:
F_friction = mass * acceleration
Rearranging the equation, we get:
acceleration = F_friction / mass
Now, substituting the known values, we have:
acceleration = (coefficient of friction * normal force) / mass
Finally, substituting the given coefficient of static friction (0.32) and the gravitational acceleration (9.8 m/s^2), the maximum acceleration that the subway car can have without the orange juice sliding backward on the floor is:
acceleration = (0.32 * mass * 9.8) / mass
The mass cancels out, resulting in:
acceleration = 0.32 * 9.8
Thus, the maximum acceleration is approximately 3.136 m/s^2.