A hungry 675 -N bear walks out on a beam in an attempt to retrieve some "goodies" hanging at the end. The beam is uniform, weighs 250 N, and is 5.00-m long; the goodies weigh 110 N.
When the bear is at x = 1.00 m, find the tension in the wire and the components of the reaction force at the hinge (left side of beam).(Tension, horizontal force on hinge, vertical force on hinge)
how is the beam attached. Where is the wire.
The wire makes a 60 degree angle from the right end of the board to the upper left. The beam is attached at a 90 degree angle to the wall on the left
To find the tension in the wire and the components of the reaction force at the hinge, we first need to consider the forces acting on the beam and the bear.
1. Forces on the beam:
- Weight of the beam (250 N) acting downward at its center of mass (midpoint of the beam).
- Reaction force at the hinge, which has horizontal and vertical components.
2. Forces on the bear:
- Weight of the bear (675 N) acting downward at its center of mass.
- Tension in the wire, which is acting upward and is exerted by the bear.
To find the tension in the wire, we need to consider the equilibrium of forces acting on the bear at x = 1.00 m.
First, let's consider the horizontal component of the reaction force at the hinge. Since the bear is not accelerating in the horizontal direction, the horizontal component of the reaction force must balance the horizontal component of the tension in the wire.
Equation 1: Horizontal component of reaction force = Horizontal component of tension in wire
Now, let's consider the vertical component of the reaction force at the hinge. Since the bear is not accelerating in the vertical direction, the vertical component of the reaction force must balance the vertical component of the tension in the wire plus the weight of the bear and the weight of the goodies.
Equation 2: Vertical component of reaction force = Vertical component of tension in wire + Weight of bear + Weight of goodies
Now, let's calculate the tension and components of the reaction force.
1. Tension in the wire:
From Equation 1, we have:
Horizontal component of reaction force = Horizontal component of tension in wire
Since the bear is at x = 1.00 m, it is not at the center of the beam. Therefore, the horizontal component of the reaction force will be non-zero.
2. Components of the reaction force at the hinge:
From Equation 2, we have:
Vertical component of reaction force = Vertical component of tension in wire + Weight of bear + Weight of goodies
Since the bear is at x = 1.00 m, the vertical component of the reaction force will be non-zero as well.
By solving these two equations simultaneously, we can find the tension in the wire and the components of the reaction force at the hinge when the bear is at x = 1.00 m.