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Deduce the magnitude of the third, unpaired force acting on the object. Useful information. The object moves at constant velocity. Two of the forces acting on the object are equal and opposite.
- Different Tensions at Different Angles. Consider the traffic light (mass of 15.0 kg) suspended from two wires as shown in Figure 6.3. Find the tension in each wire, neglecting the masses of the wires.
- Drag Force on a Barge. Two tugboats push on a barge at different angles (Figure 6.4). The first tugboat exerts a force of 2.7×105N2.7×105N in the x-direction, and the second tugboat exerts a force of 3.6×105N3.6×105N in the y-direction.
- What Does the Bathroom Scale Read in an Elevator? Figure 6.5 shows a 75.0-kg man (weight of about 165 lb.) standing on a bathroom scale in an elevator.
- Two Attached Blocks. Figure 6.6 shows a block of mass m1m1 on a frictionless, horizontal surface. It is pulled by a light string that passes over a frictionless and massless pulley.
- A box stands on a table. Identify all action-reaction forces between the box and the table.
- Identify the action-reaction force pair in each of the following situations: (a) An apple falls freely. (b) A hammer hits a nail. (c) The blades of a helicopter push air downward.
- A car is skidding to a complete stop on a horizontal road. First, identify all action-reaction pairs of forces, then show them on a free-body diagram.
- A girl exerts a force of 40 N upward to hold a box. Identify the reaction force by determining (a) its magnitude and direction, (b) on what object it is exerted, and (c) by what object it is exerted.
Practice solving for net force, using Newtons second law (F=ma), and relating F=ma to the acceleration equations. In these practice problems we will either use F=ma or our 1D motion acceleration equations to solve force problems.
- Figure \(\PageIndex{1}\): (a) A grand piano is being lifted to a second-story apartment. (b) Arrows are used to represent all forces: \(\vec{T}\) is the tension in the rope above the piano, \(\vec{F}_{T}\) is the force that the piano exerts on the rope, and \(\vec{w}\) is the weight of the piano.
- Figure \(\PageIndex{2}\): A traffic light is suspended from two wires. (b) Some of the forces involved. (c) Only forces acting on the system are shown here.
- Figure \(\PageIndex{3}\): (a) A view from above of two tugboats pushing on a barge. (b) The free-body diagram for the ship contains only forces acting in the plane of the water.
- Figure \(\PageIndex{4}\): (a) The various forces acting when a person stands on a bathroom scale in an elevator. The arrows are approximately correct for when the elevator is accelerating upward—broken arrows represent forces too large to be drawn to scale. \
As a first example of the two approaches to solving two-body problems, consider the following example problem. Example Problem 1: A 5.0-kg and a 10.0-kg box are touching each other. A 45.0-N horizontal force is applied to the 5.0-kg box in order to accelerate both boxes across the floor.
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This problem involves only motion in the horizontal direction; we are also given the net force, indicated by the single vector, but we can suppress the vector nature and concentrate on applying Newton’s second law.
