Question

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 ?k. Express your answers in terms of vi, ?k, and g only. (Assume the direction of the stone's motion to be the positive direction. Do not substitute numerical values; use variables only. Indicate the direction with the sign of your answer.)
(a) What is the acceleration of the stone as it slides down the lane?
(b) What distance does the curling stone travel?

Answer 1

Answer:

a)  a = -K g  b)    x = vi² /  2Kg

Explanation:

. a) To solve this problem we will use Newton's second law, in each axis independently

X axis

     -fr = m a

Note that the force of friction goes in the opposite direction to the initial speed, so it is negative

Y Axis  

     N-W = 0

     N = W = mg

The friction force equation is

     fr = μ N

We replace

     -μ mg = ma

      a = -μ g

The sign indicates that acceleration is opposed to movement

We replace

      a = -K g

b) for this part we use kinematic relationships

      Vf² = vi² + 2 a x

       0 = vi² - 2 a x

       x = vi² / 2 a

       x = vi² / 2 (K g)

       x = vi² / 2Kg

Answer 2

For the game similar to the lawn blowing, the curling stone has the value of acceleration and distance traveled as,

• (a) The acceleration of the stone as it slides down the lane is,

         $a=-k g$

• (b) The distance, curling stone travel is,

          $x=\dfrac{v_i^2}{2kg}$

What is Newton’s second law of motion?

Newton’s second law of motion shows the relation between the force mass and acceleration of a body. It says, that the force applied on the body is equal to the product of mass of the body and the acceleration of it.

It can be given as,

$F=ma$

Here, (m) is the mass of the body and (a) is the acceleration.

• (a) The acceleration of the stone as it slides down the lane-

The force of friction which acts in the opposite direction due to the acceleration, can be given as using the second law of motion as,

$F_r=-ma$

The force of friction is the product of coefficient of the friction and the normal force. Thus, the above equation can be written as,

$\mu F_n=-ma$

The normal force, due to the gravitational acceleration is the product of mass times gravity. Thus, the equation  can be written as,

$\mu (mg)=-ma\\a=-\mu g$

Let k is the coefficient of the friction. Thus, the acceleration of the stone as it slides down the lane is,

$a=-k g$

• (b) The distance, curling stone travel-

From the third law of equation of motion, the velocity of the particle can be given as,

$v^2-u^2=2as$

When the final velocity is zero, we get the distance of the culling stone as,

$0-(v_i)^2=2a(x)\\x=-\dfrac{v_i^2}{a}\\x=\dfrac{v_i^2}{2kg}$

Thus, he distance, curling stone travel is,

$x=\dfrac{v_i^2}{2kg}$

Thus, For the game similar to the lawn blowing, the curling stone has the value of acceleration and distance traveled as,

• (a) The acceleration of the stone as it slides down the lane is,

         $a=-k g$

• (b) The distance, curling stone travel is,

          $x=\dfrac{v_i^2}{2kg}$

Learn more about the Newton’s second law of motion here;

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