What is the mechanical advantage of the machine?
2 answers:
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Answer:
Having a bigger angle above the horizontal
Explanation:
Applying the energy conservation theorem:
The kinetic energy is reduced because of the work done by the friction force.
The friction force is given by:
so the friction force depends on the Normal force, because the slide has an angle the normal force is given by:
So when the angle of the slide is bigger, the friction force decreases, for example:
for 45 degrees:
for 75 degrees:
as you can see if the angle is bigger above the horizontal, the friction force is reduced and so the work done by that force. We didn't have to change the height of the slide, so the potential gravitational energy remains the same.
Answer:
x = 41.28 m
Explanation:
This is a projectile launching exercise, let's find the time it takes to get to the base of the cliff.
Let's start by using trigonometry to find the initial velocity
cos 25 = v₀ₓ / v₀
sin 25 = Iv_{oy} / v₀
v₀ₓ = v₀ cos 25
v_{oy} = v₀ sin 25
v₀ₓ = 22 cos 25 = 19.94 m / s
v_{oy} = 22 sin 25 = 0.0192 m / s
let's use movement on the vertical axis
y = y₀ + v_{oy} t - ½ g t²
when reaching the base of the cliff y = 0 and the initial height is y₀ = 21 m
0 = 21 + 0.0192 t - ½ 9.81 t²
4.905 t² - 0.0192 t - 21 = 0
t² - 0.003914 t - 4.2813 =0
we solve the quadratic equation
t =
t =
t₁ = 2.07 s
t₂ = -2.067 s
since time must be a positive scalar quantity, the correct result is
t = 2.07 s
now we can look up the distance traveled
x = v₀ₓ t
x = 19.94 2.07
x = 41.28 m
m = mass = 5 kg
= initial velocity = 100 m/s
= final velocity = ?
I = impulse = 30 Ns
Using the impulse-change in momentum equation
I = m( -
)
30 = 5 ( - 100)
= 106 m/s