A crane lifts a 100 kg concrete block to a vertical height of 25 m. Calculate
1 answer:
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Answer:
he sphere that uses less time is sphere A
Explanation:
Let's start with ball A, for this let's use the kinematics relations
v² = v₀² - 2g (y-y₀)
indicate that the sphere is released therefore its initial velocity is zero and when it reaches the floor its height is zero y = 0
v² = 0 - 2 g (0- y₀)
v =
v =
v = 4.427 √H
Now let's work the sphere B, in this case it rolls down a ramp, let's use the conservation of energy
starting point. At the highest point, before you start to move
Em₀ = U = m g y
final point. At the bottom of the ramp
Em_f = K = ½ m v² + ½ I w²
notice that we include the kinetic energy of translation and rotation
energy is conserved
Em₀ = Em_f
mg H = ½ m v² + ½ I w²
angular and linear velocity are related
v = w r
w = v / r
the momentorot of inertia indicates that it is worth
I = m r²
we substitute
m g H = ½ m v² + ½ ( m r²) (
)²
gH = v² +
v² =
v²
v =
v =
v=3.742 √H
Taking the final speeds of the sphere, let's analyze the distance traveled, sphere A falls into the air, so the distance traveled is H. The ball B rolls in a plane, so the distance (L) traveled can be found with trigonometry
sin θ = H / L
L = H /sin θ
we can see that L> H
In summary, ball A arrives with more speed and travels a shorter distance, therefore it must use a shorter time
Consequently the sphere that uses less time is sphere A
Refer to the diagram shown below.
At A, the boy begins walking up the stairs.
At B, the boy is at the top of the slide. He has acquired PE (potential energy).
The value of the PE is
(50 kg)*(9.8 m/s²)*(11.5 m) = 5635 J
At C, the boy has KE (kinetic energy).
The value of the KE is
(1/2)*(50 kg)*(12 m/s)² = 3600 J
Energy is lost between B and C due to friction.
The lost energy is
5635 - 3600 = 2035 J
The distance traveled along the slide is 108 m.
If F = the average frictional force, then
(F N)*(108 m) = 2035 J
F = 18.84 N
Answers:
(a) The mechanical energy lost by sliding is 2035 J.
(b) The average frictional force is 18.84 N
At A, the boy begins walking up the stairs.
At B, the boy is at the top of the slide. He has acquired PE (potential energy).
The value of the PE is
(50 kg)*(9.8 m/s²)*(11.5 m) = 5635 J
At C, the boy has KE (kinetic energy).
The value of the KE is
(1/2)*(50 kg)*(12 m/s)² = 3600 J
Energy is lost between B and C due to friction.
The lost energy is
5635 - 3600 = 2035 J
The distance traveled along the slide is 108 m.
If F = the average frictional force, then
(F N)*(108 m) = 2035 J
F = 18.84 N
Answers:
(a) The mechanical energy lost by sliding is 2035 J.
(b) The average frictional force is 18.84 N