A student pushes horizontally on a textbook of
mass 0.250 kg and holds it stationary against the
classroom wall.
a) Draw a free body diagram showing and labeling
all the forces acting on the textbook.
b) From your diagram, what is the friction force that holds the textbook in place?
c) The coefficient of static friction between book and wall is 0.190. Use this and your freebody
diagram to determine the minimum force needed to hold the textbook in place.
To answer these questions, we need to understand the forces acting on the textbook and apply Newton's laws of motion.
a) Free Body Diagram:
A free body diagram is a visual representation that shows all the forces acting on an object. In this case, the forces acting on the textbook are:
- The gravitational force (mg) acting vertically downwards, where m is the mass of the textbook and g is the acceleration due to gravity.
- The normal force (N) exerted by the wall on the textbook, which acts perpendicular to the wall.
- The friction force (f) exerted by the wall on the textbook, which acts parallel to the wall and opposes the applied force.
b) Friction Force:
From the free body diagram, we can see that the friction force is the only force opposing the applied force. In this case, since the textbook is held stationary against the wall, the friction force balances the applied force. Therefore, the value of the friction force is equal in magnitude but opposite in direction to the applied force.
c) Minimum Force to Hold the Textbook in Place:
To determine the minimum force needed to hold the textbook in place, we use the equation for static friction:
f_static = μ * N
where μ is the coefficient of static friction and N is the normal force.
From the free body diagram, we can see that the normal force is equal to the gravitational force, N = mg.
Now we can substitute these values into the equation:
f_static = μ * N = μ * (mg)
Given that the coefficient of static friction is 0.190, and the mass of the textbook is 0.250 kg, we can calculate the minimum force:
f_static = 0.190 * (0.250 kg * 9.8 m/s^2) = 0.468 N
Therefore, the minimum force needed to hold the textbook in place against the wall is 0.468 Newtons.