1. A 70 kg uniform 4.0 m long beam is attached to a vertical wall and is supported by a wire. The beam makes an angle of 45 degrees with the horizontal and the wire is horizontal. The

Question

horizontal component of the force that the wall exerts on the lower end of the beam is, in Newtons ( g = 9.8 N/kg
A) 195
B) 245
C) 232
D) 343
E) None of the above. My answer is__________________________

2. A Styrofoam box used as a picnic cooler has a surface area of 0.60 m2 and a wall thickness of
2.0 cm. The temperature inside is 5 oC, and that outside is 25 oC. It takes 10.0 hours for 5.0 kg of ice to melt in the
cooler. If the temperature outside the cooler where 20 oC, then the number of hours the 5.0 kg of ice would last is, in
hours
A) 11.7
B) 12.5
C) 13.3
D) 15.0
E) None of the above. My answer is__________________________

Answer 1

In A, write an equation for the moment about the lower end of the beam. It should tell you that the tension in the wire is twice the weight. An eq

Answer 2

In A, write an equation for the moment about the lower end of the beam. It should tell you that the tension in the wire is twice the weight. An equal but opposite force must be applied at the wall to maintain horizontal equilibrium.

In B, assume that heat is lost in proportion to the temperature difference across the Styrofoam. That decreases by a factor (20-5)/(25-5) = 3/4. Melting times should increase by about a factor 4/3. This assumes that almost all of the temperature drop between contents and outside air occurs across the Styrofoam. A more accurate analysis would consider the thermal conductivity of the Styrofoam (k), the wall thickness, and the heat transfer coefficient (h) inside and out. I would choose (C), but it is an approximation.