You have a beam balance, the kind of scales that tips from one side to the other, depending on the weight on each side. On the left side lies a kilogram of ice. On the right side lies the standard kilogram. The pans are in balance.

After a while all the ice melted.

Does the balance tip to the right, to the left, or does it remain unchanged?

What will be needed in order to restore the balance if necessary?

# Challenge Problems

# A solid sphere rolls down a roof

A solid sphere starts from rest and rolls without slipping a distance of 8 m down a roof that is inclined at 25˚. The roof’s edge is 5 m high from the ground. How far horizontally from the roof’s edge does the sphere hit the ground?

# The force required to hold a water hose

# How long would it take to fall through the center of the Earth?

# A passenger is late for a train

A passenger is late for a train. He stood at a railway station while the accelerating train passed him car by car. The passenger noticed that the last train car passed him for 8 seconds and the previous train car for 10 seconds. How long was the passenger late for the train? You should consider that the train moved with uniform acceleration and the length of the train cars is the same.

# What is the surface temperature of the planet?

# The stones in the container

A vertical container (right rectangular prism) with base area measuring 0.15 m by 0.2 m is being filled with identical small stones, each with a volume of 2*10^{-8} m^{3} and a mass of 0.05*10^{-3} kg. Assume that the volume of the empty spaces between the stones is negligible. If the height of the stones in the container increases at the rate of 3*10^{-3} m/s, at what rate does the mass of the stones in the container increase?

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