Respuesta :
Answer:
She travels 7.56 m before stopping.
Explanation:
Hi there!
According to the work-energy theorem, the magnitude of the work done by a force on a moving object to bring it to stop will be equal to the kinetic energy of the object:
W = KE
Where:
W = work
KE = kinetic energy
In this case, the force that stops the skier is the friction force. Then, the work done by friction will be:
W = Fr · d
Where:
Fr = friction force.
d = traveled distance.
The friction force is calculated as follows:
Fr = N · μ
Where:
N = normal force.
μ = coefficient of kinetic friction.
The forces acting in the vertical direction are the weight of the skier (w, downward) and the normal force (N, upward). Since the skier is not being accelerated in the vertical direction, then the sum of vertical forces is equal to zero:
∑Fy = N - w = 0 ⇒N = w
The weight is calculated as follows:
w = m · g
Where m is the mass of the skier and g is the acceleration due to gravity.
Then, the work done by friction can be expressed as follows:
W = Fr · d
W = N · μ · d
Since N = w = m · g
W = m · g · μ · d
The kinetic energy is calculated as follows:
KE = 1/2 · m · v²
Where v is the speed of the skier.
Appliyng work-energy theorem:
W = KE
m · g · μ · d = 1/2 · m · v²
Solving for d:
d = 1/2 · v² / g · μ
d = 1/2 · (5.71 m/s)² / (9.8 m/s² · 0.220)
d = 7.56 m
She travels 7.56 m before stopping.
She travels 7.56 m on the patch before stopping.
Work energy theorem:
According to the work-energy theorem, the work done (W) by a force is equal to the change in kinetic energy (ΔKE) of the object:
W = ΔKE
The work done by frictional force (F) will be:
W = Fd
where d is the traveled distance
The friction force is given by
F = μmg
where μ = 0.220 is the coefficient of kinetic friction.
Thus, the work done by friction is:
W = μmgd
Now, the change in kinetic energy is :
[tex]\Delta KE = \frac{1}{2} m (\Delta v)^2[/tex]
Applying work-energy theorem:
W = ΔKE
[tex]\mu mgd= \frac{1}{2} m (\Delta v)^2[/tex]
[tex]d = \frac{(\Delta v)^2} {\mu g}\\\\d = \frac{(5.71-0)^2} {0.220\times9.8 g}\\\\d = 7.56 \;m[/tex]
She travels 7.56 m before stopping.
Learn more about work-energy theorem:
https://brainly.com/question/13603991?referrer=searchResults
