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prohojiy [21]
3 years ago
14

A mass of 5kg starts from rest and pulls down vertically on a string wound around a disk-shaped, massive pulley. The mass of the

disk is 5kg and its radius is 2 m. What is the linear speed, in m/s, after the mass drops by 0.3 m?
a. 0.5
b. 1.5
c. 2
d. 3
e.5
Physics
1 answer:
Paha777 [63]3 years ago
8 0

Answer:

c. V = 2 m/s

Explanation:

Using the conservation of energy:

E_i =E_f

so:

Mgh = \frac{1}{2}IW^2 +\frac{1}{2}MV^2

where M is the mass, g the gravity, h the altitude, I the moment of inertia of the pulley, W the angular velocity of the pulley and V the velocity of the mass.

Also we know that:

V = WR

Where R is the radius of the disk, so:

W = V/R

Also, the moment of inertia of the disk is equal to:

I = \frac{1}{2}MR^2

I = \frac{1}{2}(5kg)(2m)^2

I = 10 kg*m^2

so, we can write the initial equation as:

Mgh = \frac{1}{2}IV^2/R^2 +\frac{1}{2}MV^2

Replacing the data:

(5kg)(9.8)(0.3m) = \frac{1}{2}(10)V^2/(2)^2 +\frac{1}{2}(5kg)V^2

solving for V:

(5kg)(9.8)(0.3m) = V^2(\frac{1}{2}(10)1/4 +\frac{1}{2}(5kg))

V = 2 m/s

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