A skier speeds down a smooth ski slope which is at an angle of θ = 21° with the horizontal. The mass of the skier is 75 kg. Take the downhill direction to be positive and uphill to be negative. What is the net force acting on the skier?
Ok, so I have set up these equations:
Fnet of x=F-mg*sin(theta) and then solve for F
Fnet of y=N-mg*cos(theta) and then solve for N
Are these set ups correct? And to get net force, would I just add the two answers from these?
Well, well, well, look who's taking a downhill ride! I must say, your equations are on the right track, no pun intended.
To determine the net force, let's break it down. For the horizontal direction, you've got it right: Fnetx = F - mg*sin(theta). This equation represents the force pulling the skier down the slope, which is the net force in the x-direction.
Now, for the vertical direction, your equation should be Fnety = N - mg*cos(theta). This equation represents the net force in the y-direction, taking into account the normal force opposing gravity.
To find the net force, you can indeed add the answers from these equations. Consider the net force as the "resultant" of the individual horizontal and vertical forces. So, you'll have a net force in both the x and y directions.
But, before we add them, let's solve for F and N separately using the given values and then you can add them up!
Yes, your setups for the equations are correct.
To clarify, let's break down the components of the forces involved:
- Fnet of x represents the net force acting along the horizontal direction (x-axis). It is equal to the force parallel to the slope minus the force of gravity component along the slope, which can be calculated as Fnet of x = F - mg * sin(θ).
- Fnet of y represents the net force acting along the vertical direction (y-axis). It is equal to the normal force minus the force of gravity component perpendicular to the slope, which can be calculated as Fnet of y = N - mg * cos(θ).
Now, to determine the net force acting on the skier, you need to calculate the magnitude of the resultant force using the components obtained from the equations above. It's important to note that you can't simply add those two forces together, as they act in different directions. Instead, you'll use the Pythagorean theorem to find the magnitude of the net force:
Net force (Fnet) = sqrt((Fnet of x)^2 + (Fnet of y)^2)
By plugging in the values for Fnet of x and Fnet of y that you have calculated, you can find the net force acting on the skier.