Question

The pulley in (Figure 1) has radius 0.160 m and a moment of inertia 0.380 kg?m2. The rope does not slip on the pulley rim.Use energy methods to calculate the speed of the 4.00-kg block just before it strikes the floor.

Answer 1

To calculate the speed of the 4.00-kg block just before it strikes the floor, we can use energy methods. The potential energy of the block is converted into kinetic energy as it falls.

Step-by-step explanation:

To calculate the speed of the 4.00-kg block just before it strikes the floor, we can use energy methods. The potential energy of the block is converted into kinetic energy as it falls. Using the work-energy theorem, we can set the initial potential energy of the block equal to the final kinetic energy:

m * g * h = 0.5 * m * v^2

where m is the mass of the block, g is the acceleration due to gravity, h is the height the block falls, and v is the final velocity of the block. Rearranging the equation and solving for v, we get:

v = sqrt(2 * g * h)

Plugging in the values given in the problem, we have:

v = sqrt(2 * 9.8 m/s^2 * 1.0 m) = 4.43 m/s