Speed v = initial speed u + acceleration a x time t
v=u+at = 2 + 4*3 = 14 m/s
The pulley is really a wheel and axle with a rope or chain attached. A pulley makes work seem easier because it changes the direction of motion to work with gravity. Let's say you have to lift a heavy load, like a bale of hay, up to the second floor of a barn. You could tie a rope to the bale of hay, stand on the second floor, and pull it straight up. Or you could put a pulley at the second floor, stand at the first floor, and lift the bale of hay by pulling straight down. It would be the exact amount of work in either case, but the action of pulling down feels easier because you're working with the force of gravity.
A pulley really saves effort when you have more than one pulley working together. By looping a rope around two, three, or even four pulleys, you can really cut down on the effort needed to lift something. The trade-off? Well, as you increase the number of pulleys, you also increase the distance you have to pull the rope. In other words, if you use two pulleys, it takes half the effort to lift something, but you have to pull the rope twice as far. Three pulleys will result in one-third the effort — but the distance you have to pull the rope is tripled!
Answer:
w = 1.14 rad / s
Explanation:
This is an angular momentum exercise. Let's define a system formed by the three bodies, the platform, the bananas and the monkey, in such a way that the torques during the collision have been internal and the angular momentum is preserved.
Initial instant. The platform alone
L₀ = I w₀
Final moment. When the bananas are on the shelf
we approximate the bananas as a point load and the distance is indicated
x = 0.45m
L_f = (m x² + I ) w₁
angular momentum is conserved
L₀ = L_f
I w₀ = (m x² + I) w₁
w₁ =
Let's repeat for the platform with the bananas and the monkey is the one that falls for x₂ = 1.73 m
initial instant. The platform and bananas alone
L₀ = I₁ w₁
I₁ = (m x² + I)
final instant. After the crash
L_f = I w
L_f = (I₁ + M x₂²) w
the moment is preserved
L₀ = L_f
(m x² + I) w₁ = ((m x² + I) + M x₂²) w
(m x² + I) w₁ = (I + m x² + M x₂²) w
we substitute
w =
w =
the moment of inertia of a circular disk is
I = ½ m_p x₂²
we substitute
w =
let's calculate
w =
w =
w = 1.14 rad / s