A 35-kg skier skis directly down a frictionless slope angled at 11° to the horizontal. Assume the skier moves in the negative direction of an x axis along the slope. A wind force with component Fx acts on the skier. What is Fx (in N) if the magnitude of the skier's velocity is.. constant? ..increasing at a rate of 1.0 m/s^2? ..increasing at a rate of 2.0 m/s^2?
Writing the sum of the forces down the slope....
Weight*sinTheta-Windfriction=mass*acceleration.
In the first part, a=0
so..
35*sin(11)-Fx=0
and solvee for Fx?
.. as for the increasing rate.. is it telling me that the 1.0m/s2 is added to the gravity of 9.8m/s2?
this is kinda late answer, but still...
35*sin(11)-Fx=0
This works for a = 0
35*sin(11)+ma-Fx=0
More complete answer... (a!=0)
So, for increasing rate of a = 1m/s^2
This is going in negative direction, so
35*sin(11)+(35)(1)=Fx
And for a = 22/s^2
35*sin(11)+(35)(2)=Fx
Crunch in calculator for Fx in Newtons
Actually, just noticed that was for in -x direction, so change sign on acceleration
35*sin(11)+(35)(-1)=Fx
35*sin(11)+(35)(-2)=Fx
ur supposed to multiply the 35sintheta with the acceleration due to gravity (9.8)
To find the wind force component acting on the skier, we can use the equation you provided:
Weight*sinTheta - Wind friction = mass * acceleration
In this equation, the weight of the skier is given by the product of mass and gravitational acceleration (mg), with a direction of down the slope. The component of weight in the direction of the slope is mg*sinTheta.
When the magnitude of the skier's velocity is constant, acceleration is zero. Therefore, the equation becomes:
35kg * sin(11°) - Fx = 0
Now, we can solve for Fx:
Fx = 35kg * sin(11°)
Fx ≈ 6.199 N
When the skier's velocity is increasing at a rate of 1.0 m/s^2, we need to consider the additional acceleration due to this change. The equation now becomes:
Weight*sinTheta - Wind friction = mass * (acceleration from slope + acceleration due to velocity increase)
Weight*sinTheta = mass * (9.8 m/s^2 + 1.0 m/s^2)
Plug in the values and calculate:
35kg * sin(11°) = 35kg * (9.8 m/s^2 + 1.0 m/s^2)
Fx ≈ 376.26 N
Similarly, for an acceleration rate of 2.0 m/s^2, we have:
35kg * sin(11°) = 35kg * (9.8 m/s^2 + 2.0 m/s^2)
Fx ≈ 377.78 N
So, the wind force component Fx is approximately 376.26 N when the skier's velocity is increasing at a rate of 1.0 m/s^2, and approximately 377.78 N when the velocity is increasing at a rate of 2.0 m/s^2.
Note: Make sure to double-check the calculations and round to the appropriate number of significant figures.