A girl is sitting in an old automobile tire which is suspended as shown. If the girl and the tire together have a mass of 60 kg. Determine the tensions in the ropes AC and BC.
Answers
Answer:
Two Blocks on an Inclined Plane
Construct the free-body diagram for object A and object B in (Figure).
Strategy
We follow the four steps listed in the problem-solving strategy.
Solution
We start by creating a diagram for the first object of interest. In (Figure)(a), object A is isolated (circled) and represented by a dot.
Figure a shows two objects on an inclined plane, sloping down to the left. Object A is on top of object B. A free body diagram shows T pointing right and up, parallel to the plane, N subscript BA pointing left and up, perpendicular to the plane, f subscript BA pointing left and down, parallel to the plane and w subscript A pointing vertically down. W subscript A is weight of block A, T is tension, N subscript BA is normal force exerted by B on A, f subscript BA is friction force exerted by B on A. Figure b shows the objects on the slope in the same manner. A free body diagram has f subscript B and f subscript AB pointing right and up, parallel to the slope, N subscript B pointing left and up perpendicular to the slope, w subscript B pointing vertically down and N subscript AB pointing down and right, perpendicular to the slope. W subscript B is weight of block B, N subscript AB is normal force exerted by A on B, N subscript B is normal force exerted by the incline plane on B. f subscript AB is friction force exerted by A on B. f subscript B is friction force exerted by the incline plane on B.
Figure 5.32 (a) The free-body diagram for isolated object A. (b) The free-body diagram for isolated object B. Comparing the two drawings, we see that friction acts in the opposite direction in the two figures. Because object A experiences a force that tends to pull it to the right, friction must act to the left. Because object B experiences a component of its weight that pulls it to the left, down the incline, the friction force must oppose it and act up the ramp. Friction always acts opposite the intended direction of motion.
We now include any force that acts on the body. Here, no applied force is present. The weight of the object acts as a force pointing vertically downward, and the presence of the cord indicates a force of tension pointing away from the object. Object A has one interface and hence experiences a normal force, directed away from the interface. The source of this force is object B, and this normal force is labeled accordingly. Since object B has a tendency to slide down, object A has a tendency to slide up with respect to the interface, so the friction
f BA is directed downward parallel to the inclined plane.
As noted of the problem-solving strategy, we then construct the free-body diagram in (Figure)(b) using the same approach. Object B experiences two normal forces and two friction forces due to the presence of two contact surfaces. The interface with the inclined plane exerts external forces of
N B and f B and the interface with object B exerts the normal force
N AB and friction f
AB is directed away from object B, and
AB is opposing the tendency of the relative motion of object B with respect to object A.
Significance
The object under consideration in each part of this problem was circled in gray. When you are first learning how to draw free-body diagrams, you will find it helpful to circle the object before deciding what forces are acting on that particular object. This focuses your attention, preventing you from considering forces that are not acting on the body.
EXAMPLE
Two Blocks in Contact
A force is applied to two blocks in contact, as shown.
Strategy
Draw a free-body diagram for each block. Be sure to consider Newton’s third law at the interface where the two blocks touch.