A child\'s hoop has mass 0.80 kg, radius 0.45 m, and moment of inertia 0.162 kg

Question

A child's hoop has mass 0.80 kg, radius 0.45 m, and moment of inertia 0.162 kg m^2. It is rolling freely on level ground at 2.80 m/s and then starts up a slope at 7 degree to the horizontal. For what distance does it travel along the slope before coming to rest? a. When a loaded ship leaves the fresh water of the St. Lawrence River and enters the denser salt water of the ocean, does it sink deeper in the water, float higher, or stay the same? Explain. b. A beaker of mass 0.040 kg containing 0.180 kg of water (density 1000 kg/m^3) sits on the pan of a balance. A piece of aluminum of volume 75 mL (75 times 10^-6 m^3) is suspended in the water from a fine thread so that it is completely submerged without touching the bottom. The density of aluminum is 2.70 times 10^3 kg/m^3. Find the total mass that is measured by the balance. A Styrofoam box has a surface area of 0.80 m^2 and a wall thickness of 2.0 cm. The temperature of the inner surface is 5.0 degree C and the outside temperature is 25 degree C. If it takes 8.0 h for 5.0 kg of ice to melt in the container, determine the thermal conductivity of Styrofoam. The latent heat of fusion of water is 3.33 times 10^5 J/kg.

Explanation / Answer

As you asked multiple questions, so l am bound to answer first one.

8.

According to conservation of energy,

(1/2)*mv^2 + (1/2)*lw^2 = mgh

(1/2)*mv^2 + (1/2)*mr^2*(v^2 / r^2) = mgh

mv^2 = mgh

h = v^2 / g

it is height acheived by hoop.

h = (2.8)^2 / 9.8 = 0.8 m

distance travelled along slop before coming rest-

d = h / sin(theta)

d = 0.8 / sin7

d = 6.56 m

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