A box is given a quick push so that it slides along a horizontal floor.
a) What is its acceleration if the coefficient of kinetic friction is 0.30?
b) How far will it travel if its initial speed was 3.0m/s?
Is it possible to find the acceleration when only one piece of information is given?
The force slowing down the box is friction
mu*mg= m*a
a= mu*g
When is work done by friction = initialKE?
mu*mg*distance= 1/2 m v^2
distance= 1/2 v^2/mu*g
Yes, it is possible to find the acceleration with only one piece of information. In this case, the coefficient of kinetic friction is given as 0.30.
To find the answers to these questions, we need to use the equation of motion relating acceleration, initial velocity, distance, and the coefficient of friction.
a) The acceleration can be found using the equation:
acceleration = coefficient of kinetic friction * acceleration due to gravity
The coefficient of kinetic friction is given as 0.30. The acceleration due to gravity is a constant value of approximately 9.8 m/s^2. So, the acceleration of the box would be:
acceleration = 0.30 * 9.8 = 2.94 m/s^2.
b) To find the distance traveled by the box, we can use the equation:
distance = (initial velocity^2) / (2 * acceleration)
The initial velocity is given as 3.0 m/s, and we have just calculated the acceleration as 2.94 m/s^2. By substituting these values into the equation, we can find the distance traveled:
distance = (3.0^2) / (2 * 2.94) = 2.55 m.
It is not possible to find the acceleration with only one piece of information. In this case, we need both the coefficient of kinetic friction and the acceleration due to gravity to find the acceleration of the box.