A block of mass m and a triangular wedge of mass M move together without slipping due to a pulling force F. The triangular wedge has a slope α. There is no friction between any pair of surfaces. Derive an equation of pulling force.

# Challenge Problems

# A system of three objects

A system is composed of three objects with masses m, 5m and 6m. The coefficient of kinetic friction between the objects m, 5m and the surface is 0.5. Find the acceleration of the objects.

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# Magnetic field due to a current in a straight wire

A corner point makes angles θ_{1} and θ_{2} with the ends of a straight wire carrying current I. The distance of the point from the wire is a. What is the

magnetic field at the point?

# The boat is pulled to the shore

A boy stands on a shore and pulls a rope connected to a boat. The velocity of the rope v_{r} is constant. Prove that the closer the boat to the shore, the faster it moves.

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

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?

# 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?