Question

A thin rod of mass M and length l hangs from a pivot at its upper end. A ball of clay of mass m and of horizontal velocity v strikes the lower end at right angles andremains stuck (total inelastic collision).

Required:
How high will the rod swing after this collision?

Answer 1

P = 2923.89 W

Step-by-step explanation:

Power is

P = F v

so This exercise will solve them in parts using the conservation of momentum and then using the conservation of energy

To use the conservation of the momentum we must define a system, formed by the bodies, so that the forces during the collision have internal forces and the moment is conserved

initial instant, before the crash

p₀ = m v

final instant. Right after the crash

`p_(f)` = (M + m) v₂

p₀ =p_{f}

m v = (M + m) v₂

v₂ = m / (m + M) v

this is the speed with which two come out, now we can apply the conservation of energy to the system formed by the two bodies together

Starting point. Lower

Em = K = ½ (M + m) v²

Final point. Highest point

Em = U = (M + m) g h

Eo₀ =
`Em_(f)`

½ (M + m) v2 = (M + m) g h

h = 1/2 v2 / g

h = ½ [m / (m + M) v] 2 / g

h = 1/2 (m / m + M) 2 / g we must calculate the force, let's use Newton's second law, let's set a coordinate system with a parallel axis flat and the other axis (y) perpendicular to the plane

X Axis

Fe - Wₓ = 0

F = Wₓ

Y Axis

N -
`W_(y)` = 0

let's use trigonometry for the components of the weight

sin 6 = Wₓ / W

cos 6 =
`W_(y)` / W

Wx = W sin 6

W_{y}= W cos 6

F = mg cos 6

F = 75 9.8 cos 6

F = 730.97 N

let's calculate the power

P = F v

P = 730.97 4.0

P = 2923.89 W