A hockey puck is hit on a frozen lake and starts moving with a speed of 14.4 m/s. 3.0 seconds later, its speed is 7.3 m/s.
(b) What is the average value of the coefficient of kinetic friction between puck and ice?
First, find the acceleration:
7.3 = 14.4 - a*t
Substitute 3 seconds into the above equation to find the acceleration a. This acceleration is due to the force of friction = ckf*m*g
where ckf is the coefficient of kinetic friction, m is the mass of the puck, and g is the acceleration due to gravity
m*a = ckf*m*g
ckf = a/g
To find the average value of the coefficient of kinetic friction between the puck and the ice, we need to use the equation relating the acceleration, change in velocity, and time:
average acceleration (a) = change in velocity (Δv) / time taken (Δt)
First, let's calculate the change in velocity:
Δv = final velocity - initial velocity
= 7.3 m/s - 14.4 m/s
= -7.1 m/s (negative sign indicates deceleration)
Next, we can substitute the values into the equation to find the average acceleration:
a = Δv / Δt
= -7.1 m/s / 3.0 s
= -2.37 m/s²
The negative sign indicates that the puck is decelerating.
Now, we can use the formula for the acceleration due to friction:
acceleration due to friction (af) = μ * g
where μ is the coefficient of kinetic friction and g is the acceleration due to gravity (approximately 9.8 m/s²).
Rearranging the formula, we get:
μ = af / g
Plugging in the values, we have:
μ = -2.37 m/s² / 9.8 m/s²
= -0.242
The average value of the coefficient of kinetic friction between the puck and the ice is approximately -0.242. Note that the negative sign indicates that the friction force is acting against the direction of motion.