Curling is a game similar to lawn bowling except it is played on ice and instead of rolling balls on the lawn, stones are slid along ice. A curler slides a stone across a sheet of ice with an initial speed vi in the positive x direction. The coefficient of kinetic friction between the stone and the curling lane is μk. Express your answers in terms of vi, μk, and g only. a. What is the acceleration of the stone as it slides down the lane? b. What distance does the curling stone travel?
(a)
The acceleration of the stone as it slides down the lane.
Answer to Problem 27PQ
The acceleration of the stone as it slides down the lane is
Explanation of Solution
Take horizontal direction to be
The stone slides on a horizontal surface so that the net force in the vertical direction must be zero.
Write the expression for the Newton’s second law of motion in
Here,
Write the expression for
Here,
Put the above equation in equation (I).
Write the expression for the Newton’s second law of motion in
Here,
Rewrite the above equation for
After the stone loses contact with the curling stick, the only force acting in the horizontal direction is the force of friction. The force of friction acts opposite to the motion of the stone.
Write the expression for
Here,
Write the expression for
Here,
Put equation (II) in the above equation.
Put the above equation in equation (IV).
Put the above equation in equation (III).
The acceleration acts along
Here,
Conclusion:
Put equation (V) in equation (VI).
Therefore, the acceleration of the stone as it slides down the lane is
(b)
The distance travelled by the curling stone.
Answer to Problem 27PQ
The distance travelled by the curling stone is
Explanation of Solution
Write the Newton’s constant acceleration equation.
Here,
Rewrite the above equation for
Put equation (V) in the above equation.
Conclusion:
The final velocity of the stone is zero.
Substitute
Therefore, the distance travelled by the curling stone is
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