An aeroplane makes in emergency landing without landing gear. If the aeroplane touches down with a horizontal speed of 60.0ms^-1 and the coefficient of friction for aluminium on asphalt is μ = 0.500, how far will the aeroplane slide before coming to rest? You may assume that acceleration due to gravity is 10.0ms^-2 and that air resistance is negligible.
Fp = Mg*sin 0 = 0.
Fn = Mg*Cos 0 = Mg = Normal force.
Fk = u*Fn = 0.50*Mg.
Fp-Fk = M*a.
0-0.5Mg = M*a, Divide by Mg:
-0.5 = a/g = a/-10, a = 5 m/s^2.
V^2 = 60^2 - 10d.
0 = 3600 -10d, d = 360 m.
Fp = Force parallel to the surface.
To find the distance the airplane slides before coming to rest, we need to determine its deceleration. We can use the concept of friction to calculate this.
The force of friction can be calculated using the formula:
Frictional force (F) = coefficient of friction (μ) * normal force (N)
The normal force (N) equals the weight of the airplane, which is the product of mass (m) and acceleration due to gravity (g).
Weight (W) = m * g
Next, we need to calculate the deceleration (a) of the airplane using Newton's second law of motion:
F = m * a
Since the force of friction is opposing the motion, it will act in the direction opposite to the horizontal speed of the airplane. Therefore, the deceleration will be negative.
Now let's put it all together:
1. Calculate the weight of the airplane:
Weight (W) = m * g
2. Calculate the frictional force:
Frictional force (F) = μ * W
3. Calculate the deceleration:
F = m * a
Rearrange the formula to solve for deceleration (a):
a = F / m
4. Calculate the time taken to come to rest:
We can use the formula:
v = u + a * t
where:
v = final velocity (0 m/s, as the airplane comes to rest)
u = initial velocity (60.0 m/s)
a = deceleration (negative value, obtained in the previous step)
t = time
Rearrange the formula to solve for time (t):
t = (v - u) / a
5. Calculate the distance traveled (s) by the airplane:
Using the formula:
s = u * t + (1/2) * a * t^2
Now, let's substitute the given values and calculate the distance traveled:
Given:
- Initial velocity (u) = 60.0 m/s
- Coefficient of friction (μ) = 0.500
- Acceleration due to gravity (g) = 10.0 m/s^2
Step 1: Calculate weight (W)
W = m * g
Step 2: Calculate frictional force (F)
F = μ * W
Step 3: Calculate deceleration (a)
a = F / m
Step 4: Calculate time (t)
t = (v - u) / a
Step 5: Calculate distance traveled (s)
s = u * t + (1/2) * a * t^2
By substituting the given values and solving these equations, we can find the distance the airplane slides before coming to rest.