A skier slides horizontally along the snow for a distance of 11.9 m before coming to rest. The coefficient of kinetic friction between the skier and the snow is 0.0458. Initially, how fast was the skier going?
I do not know how to start this. Thank you.
ΔKE =KE2 –KE1 = 0 -m•v²/2.
W(fr) =μ•m•g•s•cosα,
where α is the angle between the friction force and displacement.
α =180º, cos α = -1.
-m•v²/2 = - μ•m•g•s,
v = sqrt(2•μ• g•s).
So for v would I do sqrt(2*11.9*9.8*0.0458) ?
To solve this problem, you can use the equation of motion for a sliding object:
v^2 = u^2 + 2as
where:
- v is the final velocity of the skier (which is zero since the skier comes to rest),
- u is the initial velocity of the skier (what we want to find),
- a is the acceleration of the skier, and
- s is the distance the skier slides.
In this case, we know the final velocity is zero, and we have the distance the skier slides (11.9 m). We need to find the acceleration.
The force of friction can be calculated using the equation:
f = μN
where:
- f is the force of friction,
- μ is the coefficient of kinetic friction (given as 0.0458 in this case), and
- N is the normal force.
Since the skier is sliding horizontally, the normal force is equal to the weight of the skier, which can be calculated using the equation:
N = mg
where:
- m is the mass of the skier, and
- g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this problem, the mass of the skier is not given, so we cannot directly calculate the acceleration due to friction. However, we can cancel out the mass by dividing both sides of the force of friction equation by the mass:
f / m = μN / m
Since f / m is equal to the acceleration of the skier (a), we can rewrite the equation as:
a = μg
Now we have the acceleration, and we can substitute the known values into the equation of motion to find the initial velocity:
0 = u^2 + 2a(11.9)
Substituting the values, we have:
0 = u^2 + 2(0.0458)(9.8)(11.9)
Now you can solve this equation to find the initial velocity (u).