Consider a large textbook with mass m = 6 lb = 2.72 kg at rest sitting on a wooden table. (a.) Draw a free-body diagram for this stationary textbook. Make sure to include all the forces acting on the textbook, and clearly indicate in your diagram the net force (To be clear about it, I’m just looking for an algebraic expression of either F⃗net = m⃗a or F⃗net = 0 to appear in the diagram. I’m not looking for a number here). Also make sure to include a net force vector in your diagram (if F⃗net ̸= 0). (b.) Now, suppose one side of this table is lifted up with a pulley and fixed in place so that the table effectively acts like/becomes an inclined plane (that is, a ramp). The angle of the incline, measured from the horizontal, is measured to be 30◦. Assume the table is NOT frictionless. Take the coefficients of static and kinetic friction between the book and table to be μs = 0.4 and μk = 0.2, respectively. Assume that this angle is large enough such that the book overcomes static friction and begins to slip down the incline. Ignore air resistance.Draw a free-body diagram for the book in its new situation. (c.) Does the book actually overcome static friction and begin to slide down the slope? Let’s find out: (i.) Use your free-body diagram from the previous part and apply Newton’s Second Law. Assume static friction holds up and keeps the book from slipping until you can show otherwise. The two Newton’s Second Law component equations you get will allow you to compute the magnitude of the normal force acting on the book and components of the book’s acceleration vector. Compute the magnitude of the normal force and the components of the book’s acceleration. (ii.) Use the magnitude of the normal force that you computed to determine whether or not the book will overcome static friction and slip. Does it slip or stay in place?
Consider a large textbook with mass m = 6 lb = 2.72 kg at rest sitting on a wooden table.
(a.) Draw a free-body diagram for this stationary textbook. Make sure to include all the forces acting on the textbook, and clearly indicate in your diagram the net force (To be clear about it, I’m just looking for an algebraic expression of either F⃗net = m⃗a or F⃗net = 0 to appear in the diagram. I’m not looking for a number here). Also make sure to include a net force vector in your diagram (if F⃗net ̸= 0).
(b.) Now, suppose one side of this table is lifted up with a pulley and fixed in place so that the table effectively acts like/becomes an inclined plane (that is, a ramp). The angle of the incline, measured from the horizontal, is measured to be 30◦. Assume the table is NOT frictionless. Take the coefficients of static and kinetic friction between the book and table to be μs = 0.4 and μk = 0.2, respectively. Assume that this angle is large enough such that the book overcomes static friction and begins to slip down the incline. Ignore air resistance.Draw a free-body diagram for the book in its new situation.
(c.) Does the book actually overcome static friction and begin to slide down the slope? Let’s find out:
(i.) Use your free-body diagram from the previous part and apply Newton’s Second Law. Assume static friction holds up and keeps the book from slipping until you can show otherwise. The two Newton’s Second Law component equations you get will allow you to compute the magnitude of the normal force acting on the book and components of the book’s acceleration vector. Compute the magnitude of the normal force and the components of the book’s acceleration.
(ii.) Use the magnitude of the normal force that you computed to determine whether or not the book will overcome static friction and slip. Does it slip or stay in place?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
