If the puck strikes the goalie's pads and stops in a distance of 4.14 cm, what average force is exerted on the pads? Answer in units of N.
This is part three of three parts.
1st Part: A player strikes a hockey puck giving it a velocity of 39.486 m/s. The puck slides across the ice for 0.231s after which time its velocity is 38.666 m/s. The acceleration of gravity is 9.8 m/s^2. If the mass of the puck is 209 g, what is the average drag force on it by the ice? The answer is: -0.74190 N.
2nd Part: What is the coefficient of kinetic friction for the puck sliding on ice? The answer is 0.3622228112.
I would REALLY appreciate any help! Thanks<3
Sure, I'd be happy to help! But before we move on to the third part, I must warn you that my humor may not be everyone's cup of tea. So, if you're ready for some hilariously informative answers, let's dive right into it!
In the first two parts, we calculated the average drag force on the puck (-0.74190 N) and the coefficient of kinetic friction (0.3622228112). Now, in this third part, we'll determine the average force exerted on the goalie's pads when the puck strikes them.
Given that the puck comes to a stop in a distance of 4.14 cm, we can assume that the friction force between the pads and the puck is responsible for this deceleration. Since we have the coefficient of kinetic friction, we can use it in combination with the mass of the puck to find the force exerted on the pads.
Using the formula: force = mass * acceleration, we can rearrange it to: force = mass * deceleration.
The deceleration of the puck can be found using the equation: deceleration = change in velocity / time taken.
Since we know the initial velocity (39.486 m/s) and final velocity (0 m/s), we can replace the change in velocity with 39.486 m/s in the equation.
Now let's plug the values in and solve it step by step:
deceleration = 39.486 m/s / 0.231 s
deceleration = 171.152173913 m/s²
Now, let's calculate the force using the equation:
force = mass * deceleration
force = 0.209 kg * 171.152173913 m/s²
force = 35.73947974 N
So, the average force exerted on the goalie's pads when the puck strikes them is approximately 35.739 N.
Voila! We've reached the end of our journey through the calculations. I hope my humor didn't make you want to give me the cold shoulder. Good luck with your hockey adventures, and remember, even if you're on thin ice, it's always better to skate with a smile!
To find the average force exerted on the goalie's pads, you can use the equation for average force:
Average Force = Change in momentum / Time
Since the mass and initial and final velocities of the puck are not given in this part of the question, we will use the information from the previous parts.
From the first part of the question, we know the initial velocity of the puck is 39.486 m/s and the final velocity is 38.666 m/s. The mass of the puck is 209 g, which is equivalent to 0.209 kg.
The change in momentum can be calculated as:
Change in momentum = mass * (final velocity - initial velocity)
Change in momentum = 0.209 kg * (38.666 m/s - 39.486 m/s)
Change in momentum = -0.16766 kg·m/s
Now, we need to figure out the time it took for the puck to reach the goalie's pads. This information is not given directly, but we can assume that it took the same amount of time to travel the 4.14 cm distance as it did to slide across the ice.
From the second part of the question, we know that the coefficient of kinetic friction between the puck and the ice is 0.3622228112. And we have the initial velocity of 39.486 m/s.
We can use the following equation of motion:
Distance = (initial velocity * time) + (1/2) * (coeff. of friction) * (acceleration * time^2)
Rearranging the equation gives us:
(time^2) * (0.5 * coeff. of friction * acceleration) + (initial velocity * time) - Distance = 0
Plugging in the values and solving for time gives us:
(0.5 * 0.3622228112 * 9.8 * time^2) + (39.486 * time) - 0.0414 = 0
Solving the quadratic equation, we find that the positive value for time is approximately 0.0218 seconds.
Now we can calculate the average force:
Average Force = Change in momentum / Time
Average Force = -0.16766 kg·m/s / 0.0218 s
Average Force ≈ -7.6827 N
However, since the question asks for the force exerted on the goalie's pads, the magnitude of the force is considered. Therefore, the average force exerted on the pads from the puck is approximately 7.6827 N.
To find the average force exerted on the goalie's pads, we can use the equation for average force:
Average Force = (Final Momentum - Initial Momentum) / Time
1. First, we need to find the initial momentum of the puck. Momentum is defined as mass times velocity:
Initial Momentum = Mass * Initial Velocity
Given the mass of the puck is 209 g (0.209 kg) and the initial velocity is 39.486 m/s, we can calculate:
Initial Momentum = 0.209 kg * 39.486 m/s
2. Next, we need to find the final momentum of the puck. Since the puck stops after striking the goalie's pads, the final momentum is zero.
Final Momentum = 0
3. We also know the time it takes for the puck to stop is 0.231 s.
Now, we can plug the values into the equation for average force:
Average Force = (Final Momentum - Initial Momentum) / Time
= (0 - (0.209 kg * 39.486 m/s)) / 0.231 s
Calculate the value in the parenthesis:
Initial Momentum = 0.209 kg * 39.486 m/s
Now:
Average Force = (0 - (0.209 kg * 39.486 m/s)) / 0.231 s
Simplify:
Average Force = (-0.209 kg * 39.486 m/s) / 0.231 s
Calculate:
Average Force = - 0.74190 N
So, the average force exerted on the goalie's pads is -0.74190 N. The negative sign indicates that the force is in the opposite direction of the initial momentum.
(a)
v=v₀-at
a=( v-v₀)/t=(38.666-39.486)/0.231 =-3.55 m/s²
F(dr)=ma=-0.209•(-3.55)=-0.7419 N
(b)
F(dr)=μN=μmg
μ=F(dr)/mg=0.7419/0.209•9.8=0.362
(c)
Work-energy theorem
ΔKE=W(dr)
0-mv²/2=F•s.
F= - mv²/2s= - 0.209• 39.486²/2•0.041=-3935N