Hockey Puck With only one speed

[Hypnos_16]

Homework Statement

In attempting to pass the puck to a teammate, a hockey player gives it an initial speed of 1.91 m/s. However, this speed is inadequate to compensate for the kinetic friction between the puck and the ice. As a result, the puck travels only one-half the distance between the players before sliding to a halt. What minimum initial speed should the puck have been given so that it reached the teammate, assuming that the same force of kinetic friction acted on the puck everywhere between the two players?

v1 = 1.91
d = 1/2 way

Homework Equations

it seems I'm not given anything to solve this question, and I'm just straight up confused as to what i need to even start this question

The Attempt at a Solution

i don't really have an attempt, i can't get anything to work here, someone please help, or even explain what's happening here.

 

[Doc Al]

Hint: Consider the work done by friction.

 

[Hypnos_16]

I know that friction plays a role but i don't know anything about it, besides that it opposes the puck.

 

[Doc Al]

I know that friction plays a role but i don't know anything about it, besides that it opposes the puck.

All you need to know about the friction is that it's constant. And my earlier hint.

 

[rwisz]

I understand that this situation involves the concept of kinetic friction, which is the force that opposes the motion of the puck on the ice surface. Based on the given information, the initial speed of the puck (v1) is not enough to overcome the force of kinetic friction and reach the teammate. This results in the puck only traveling half the distance between the players before coming to a stop.

To determine the minimum initial speed needed for the puck to reach the teammate, we can use the equation for kinetic friction: Fk = μkN, where Fk is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force.

Since the force of kinetic friction is acting on the puck everywhere between the two players, we can assume that the coefficient of kinetic friction and the normal force remain constant. Therefore, the only variable we need to consider is the initial speed of the puck.

We can use the equation for distance traveled (d = v1^2/2a) to determine the distance the puck travels before stopping. In this case, we know the distance traveled is only half of the total distance between the players (d/2). We also know the acceleration (a) is equal to the force of kinetic friction divided by the mass of the puck (a = Fk/m).

Combining these equations, we can set up the following equation to solve for the minimum initial speed (v1) needed for the puck to reach the teammate:

d/2 = (v1^2)/(2(Fk/m))

Solving for v1, we get:

v1 = √(d(Fk/m))

Substituting in the given values, we get:

v1 = √(1/2 * (1.91)^2 * (Fk/m))

From here, we can use the given initial speed (1.91 m/s) to calculate the force of kinetic friction (Fk) and the mass of the puck (m). Once we have these values, we can plug them back into the equation to solve for the minimum initial speed needed for the puck to reach the teammate.

In summary, to solve this problem we need to consider the concepts of kinetic friction, distance traveled, and acceleration. By setting up and solving an equation, we can determine the minimum initial speed needed for the puck to reach the teammate.