Physics Homework Question?

Question

A ball is attached to a horizontal cord of length L, whose other end is fixed.

1.) If the ball is released, what will its speed be at the lowest point of its path?

2.) A peg is located at a distance h directly below the point of attachment of the cord. If h=0.8L, what will be the speed of the ball when it reaches the top of its circular path about the peg?

Answer 1

A ball is attached to the horizontal cord of length L.

(1)

Find the speed of the ball at the lowest point of its path, when it is released.

Use law of conservation of energy to determine the speed of the ball at lowest path.

Total mechanical energy equal the sum of kinetic and potential energies of the objects.

.

Draw the diagram for the situation:

Observe the figure:

At point 1,  

At point 2,   .

Therefore, the speed of the ball at lowest point in its path is .

Answer 2

A ball is attached to the horizontal cord of length L.

(2)

A peg is located at h units below the point of attachment of the cord such that .

Draw the figure for the situation.

Observe the graph,

Height above the ball to peg is .

Hence the radius of the circle is .

Therefore, the diameter of the circular path about the peg is .

Find the speed of the ball when it reaches top of the circular path at point 2.

From the law of conservation of energy:

At point 1,  .

At point 2,  .

Therefore, the speed of the ball at the top of the circular path about the peg is .