What Force is Needed to Push a 40kg Sled on Ice with μk = 0.05?

[Shinster007]

Homework Statement

The first problem I am having trouble with is as follows:

A child pushes a 40kg sled across the ice at a constant speed. If μk = 0.05 calculate the force applied to the sled.

Homework Equations

I know that f=$\mu$F_N

The Attempt at a Solution

I know that the free body diagram would consist of a point with a direction in the x coordinate, but I have no idea how to go about this problem. Math and physics is not my strong subject; this is my first ever physics class

 

[CAF123]

Have you tried drawing the free body diagram? The sled is moving at constant speed so the net force acting on it is zero.

 

[Shinster007]

Here is what I came up with:

Ʃ_y=F_N-mg=0. Therefore, F_N=mg=(40kg)*(9.8 m/s²)=392N.

Ʃ_x=F-f=0. Therefore, F=f, which equals $\mu$_s*F_N, which equals (0.05)*(392N), giving me an answer of 19.6N. Did I do this correctly?

 

[CAF123]

Yes.

 

[Shinster007]

Okay thanks for the help, I am feeling kinda dumb now that I know it is that simple.

Next question:

A 60kg snowboarder accelerates down a 32 degree slope at 3.0m/s2. Calculate μk.

Attempt:

Obviously since there is an acceleration, I know that the forces in the x direction acting on the snowboarder do not equal zero. When setting up a free body diagram I have F_N acting upward, F_g acting "downward" (but not on the y axis), then F_x in the positive x direction, and f_x in the negative direction.

I then get the following:

Ʃ_y= F_N-mg*cos∅=0;
so F_N=(60kg*9.8m/s²)*(cos 32)=498N.

Ʃ_x=mg*sin∅-$\mu$_kF_N=ma.

Is this correct so far? Would it then just be a matter of moving everything around algebraically and solving for $\mu$_k?

 

[Shinster007]

Oops, *centripetal

 

[CAF123]

Okay thanks for the help, I am feeling kinda dumb now that I know it is that simple.

Next question:

A 60kg snowboarder accelerates down a 32 degree slope at 3.0m/s2. Calculate μk.

Attempt:

Obviously since there is an acceleration, I know that the forces in the x direction acting on the snowboarder do not equal zero. When setting up a free body diagram I have F_N acting upward, F_g acting "downward" (but not on the y axis), then F_x in the positive x direction, and f_x in the negative direction.

I then get the following:

Ʃ_y= F_N-mg*cos∅=0;
so F_N=(60kg*9.8m/s²)*(cos 32)=498N.

Ʃ_x=mg*sin∅-$\mu$_kF_N=ma.

Is this correct so far? Would it then just be a matter of moving everything around algebraically and solving for $\mu$_k?

Yes, simply solve for $\mu_k$

 

[Shinster007]

Okay, getting the hang of this.

Last question:

A baseball player initially running at 3.4m/s slides to a stop at third base in 1.2 seconds. Calculate the μk between him and the ground.

Attempt:

I'm not sure how to approach this problem. 3.4m/s divided by the 1.2s will give me the acceleration I think (or I guess deceleration in this case). Other than that I am at a loss

 

[CAF123]

Okay, getting the hang of this.

Last question:

A baseball player initially running at 3.4m/s slides to a stop at third base in 1.2 seconds. Calculate the μk between him and the ground.

Attempt:

I'm not sure how to approach this problem. 3.4m/s divided by the 1.2s will give me the acceleration I think (or I guess deceleration in this case). Other than that I am at a loss

The frictional force provides the negative acceleration, necessary for him to come to a stop. Using the negative acceleration calculated above, you can find $\mu_k.$

 

[Shinster007]

Well I know that f=$\mu$_k*F_N, but I don't have a mass in order to calculate F_N, nor do I have f. What equation can I use to solve the problem?

 

[CAF123]

Well I know that f=$\mu$_k*F_N, but I don't have a mass in order to calculate F_N, nor do I have f. What equation can I use to solve the problem?

Simply use $F = ma.$ You know the only force acting horizontally on the baseball player as he slides (force of friction). This is your $F.$ Now sub in what $F$ is equal to and what do you notice about $m$?

 

[vela]

Well I know that f=$\mu$_k*F_N, but I don't have a mass in order to calculate F_N, nor do I have f. What equation can I use to solve the problem?

Your teacher probably encourages you to work problems out using symbols first and plug numbers in at the end. This is one of the reasons why.