15. An official NHL hockey puck must have a mass between 156 g and 170 g . Your hockey puck has a mass of 170 g and is shot north along the ice at $$ 3.0 \mathrm{~m} / \mathrm{s} $$. If after travelling $$ 8,0 \mathrm{~m} $$ the puek comes to rest, determine the force of friction that acted on the puck, $$ [0,096 \mathrm{~N} $$, south $$ ] $$

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To determine the force of friction that acted on the hockey puck, we can use the concept of work and energy. The work done by the force of friction is equal to the change in kinetic energy of the puck.

Given:
- Initial mass of the puck: 170 g
- Initial velocity of the puck: 3.0 m/s
- Distance traveled by the puck: 8.0 m
- Final velocity of the puck: 0 m/s (comes to rest)

First, we need to convert the mass of the puck from grams to kilograms:
$$ 170 \, \text{g} = 0.17 \, \text{kg} $$

Next, we can calculate the initial kinetic energy of the puck:
$$ \text{Initial kinetic energy} = \frac{1}{2} \times m \times v^2 $$
$$ \text{Initial kinetic energy} = \frac{1}{2} \times 0.17 \, \text{kg} \times (3.0 \, \text{m/s})^2 $$

Then, we can calculate the work done by the force of friction:
$$ \text{Work done by friction} = \text{Initial kinetic energy} - \text{Final kinetic energy} $$
$$ \text{Work done by friction} = \text{Initial kinetic energy} - 0 $$

Finally, we can calculate the force of friction using the formula:
$$ \text{Force of friction} = \frac{\text{Work done by friction}}{\text{Distance traveled}} $$

Let's calculate the force of friction.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{2}\times 0.17\times 3^{2}$$
- step1: Multiply the terms:
  $$\frac{17}{200}\times 3^{2}$$
- step2: Multiply:
  $$\frac{17\times 3^{2}}{200}$$
- step3: Multiply:
  $$\frac{153}{200}$$
The initial kinetic energy of the puck is $$ \frac{153}{200} $$ J or approximately 0.765 J.

Now, we can calculate the work done by the force of friction:
$$ \text{Work done by friction} = \text{Initial kinetic energy} - \text{Final kinetic energy} $$
$$ \text{Work done by friction} = 0.765 \, \text{J} - 0 \, \text{J} = 0.765 \, \text{J} $$

Next, we can calculate the force of friction:
$$ \text{Force of friction} = \frac{\text{Work done by friction}}{\text{Distance traveled}} $$
$$ \text{Force of friction} = \frac{0.765 \, \text{J}}{8.0 \, \text{m}} $$

Let's calculate the force of friction.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{0.765}{8}$$
- step1: Convert the expressions:
  $$\frac{\frac{153}{200}}{8}$$
- step2: Multiply by the reciprocal:
  $$\frac{153}{200}\times \frac{1}{8}$$
- step3: Multiply the fractions:
  $$\frac{153}{200\times 8}$$
- step4: Multiply:
  $$\frac{153}{1600}$$
The force of friction acting on the hockey puck is approximately 0.095625 N, which is directed south.
The force of friction acting on the hockey puck is approximately 0.096 N, directed south.

An official NHL hockey puck must have a mass between 156 g and 170 g . Your hockey puck
has a mass of 170 g and is shot north along the ice at . If after travelling the puek
comes to rest, determine the force of friction that acted on the puck, , south

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An official NHL hockey puck must have a mass between 156 g and 170 g . Your hockey puck has a mass of 170 g and is shot north along the ice at . If after travelling the puek comes to rest, determine the force of friction that acted on the puck, , south