Final answer:
To calculate the time it takes for the hockey puck to stop sliding, calculate the friction force, deceleration, and then use the formula for time. The time it takes for the puck to stop sliding can then be calculated using the formula: Time = Initial velocity / Deceleration.
Step-by-step explanation:
To calculate the time it takes for the hockey puck to stop sliding, we need to determine the deceleration of the puck caused by the friction between the puck and the rough ice.
The formula for the force of friction is given by: Friction force = coefficient of friction × normal force.
The normal force is equal to the weight of the puck, which can be calculated as: Normal force = mass × acceleration due to gravity.
Using the given values, the coefficient of kinetic friction is 0.25, the mass of the puck is 0.20 kg, and the acceleration due to gravity is approximately 9.8 m/s².
Substituting these values into the formula, we get: Friction force = 0.25 × (0.20 kg × 9.8 m/s²).
The friction force acts in the opposite direction to the motion of the puck, causing it to decelerate. The deceleration can be calculated using the formula: Deceleration = Friction force / mass.
Substituting the values obtained, we get: Deceleration = (0.25 × (0.20 kg × 9.8 m/s²)) / 0.20 kg.
The time it takes for the puck to stop sliding can then be calculated using the formula: Time = Initial velocity / Deceleration.
Substituting the given initial velocity of 1.2 m/s and the calculated deceleration, we get: Time = 1.2 m/s / ((0.25 × (0.20 kg × 9.8 m/s²)) / 0.20 kg). Solving this equation gives us the time it takes for the puck to stop sliding.