New wax on her skis allows 55 kg mass Terri to glide frictionless down an icy bunny hill from rest, over a distance of 9.0 m, before reaching the flat bottom with a final velocity of 10.05 m/s.
Create a FBD for Terri
Find the net acceleration of Terri
Find the angle of the hill
Find the normal force of the hill
Since Terri does not know how to stop she just allows the friction of the flat wet snow to slow her with a force of Ff = 66 N. What is her new horizontal acceleration?
How much time passes before she comes to rest
To create a Free Body Diagram (FBD) for Terri, we need to consider the forces acting on her.
1. Force of Gravity (Fg): acting vertically downward with a magnitude of mg, where m is Terri's mass (55 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Normal Force (Fn): the force exerted by the surface on Terri perpendicular to the surface. It acts vertically upward and cancels out the vertical component of the force of gravity.
3. Friction Force (Ff): acting horizontally in the opposite direction of Terri's motion. Given as 66 N.
Next, let's find the net acceleration (a) of Terri:
Using the formula for net force (Fnet = ma), we can calculate the net force acting on Terri.
The net force is equal to the force of friction (Ff) since there are no other horizontal forces present.
Ff = ma
66 N = (55 kg) * a
Solving for a, we get:
a = 66 N / 55 kg
a ≈ 1.2 m/s^2
Now, let's find the angle of the hill (θ):
The angle of the hill (θ) can be determined using the equation:
tan(θ) = a / g
Substituting the values, we get:
tan(θ) = 1.2 m/s^2 / 9.8 m/s^2
Taking the inverse tangent (arctan) of both sides, we find:
θ = arctan(1.2 / 9.8)
θ ≈ 7.27 degrees
The normal force (Fn) can be calculated using the equation:
Fn = mg * cos(θ)
Substituting the given values, we get:
Fn = (55 kg) * 9.8 m/s^2 * cos(7.27 degrees)
Fn ≈ 530 N
Next, let's find Terri's new horizontal acceleration:
Since Terri is slowing down with a horizontal frictional force (Ff) of 66 N, we can use Newton's second law (Fnet = ma) to find her new horizontal acceleration.
Ff = ma
66 N = (55 kg) * a
Solving for a, we get:
a = 66 N / 55 kg
a ≈ 1.2 m/s^2
The time it takes for Terri to come to a stop can be found using the equation:
v = u + at
where:
v = final velocity (0 m/s since she comes to rest)
u = initial velocity (10.05 m/s)
a = acceleration (-1.2 m/s^2, negative since it opposes the initial velocity)
t = time
Rearranging the equation, we get:
t = (v - u) / a
t = (0 m/s - 10.05 m/s) / -1.2 m/s^2
t ≈ 8.38 s
Therefore, it takes approximately 8.38 seconds for Terri to come to a stop.