Question

Two crates are attached by a rope over a light, frictionless pulley. The left crate has mass mi = 2 kg and rests on a surface. The right create has mass m2 = 5 kg and sits at height h. mal h m, The crates are allowed to move and the right crates strikes the ground at 8 m/s. What is the height h in m? Enter answer here 7. 2b What is the total mechanical energy in J? Enter answer here 8. 2c If you consider the rate of transfer of energy between potential and kinetic energy, what is the magnitude of that power as the right mass strikes the table in W?

Answer 1

To find the height h, equate the potential energy at height h with the kinetic energy at the moment the crate strikes the ground. The total mechanical energy remains constant and equals the initial potential energy. Calculating power as the rate of energy transfer is not possible without the time duration for the fall.

Step-by-step explanation:

The question involves finding the height from which a crate falls to reach a velocity of 8 m/s using principles from physics, specifically kinetic and potential energy, as well as the conservation of mechanical energy.

The formula for gravitational potential energy (Potential Energy) is PE = m*g*h where m is mass, g is the acceleration due to gravity (9.81 m/s2 on Earth), and h is the height.

The formula for kinetic energy (Kinetic Energy) is KE = 0.5*m*v2 where v is velocity.

By setting the potential energy equal to the kinetic energy at the moment right before the crate hits the ground, we can solve for the height h.

The total mechanical energy in the system remains constant if we ignore air resistance and assume a frictionless pulley.

The total mechanical energy (Total Mechanical Energy) is the sum of potential and kinetic energy.

Since the crate starts at rest, and at height h, all of its initial mechanical energy is potential energy, which converts to kinetic energy as the crate falls.

Answer 2

(a) The height of fall of the crates is 3.27 m.

(b) The total mechanical energy is 224 J.

(c) The magnitude of that power as the right mass strikes the table is 273.2 W.

How to calculate the height of the crates?

(a) The height of fall of the crates is calculated by applying the principle of conservation of energy as follows.

P.E (at top) = K.E (at bottom)

mgh = ¹/₂mv²

gh = ¹/₂v²

h = (v²) / 2g

where;

• v is the speed of the crate when it hits the ground
• g is acceleration due to gravity

h = (v²) / 2g

h = ( 8² ) / (2 x 9.8)

h = 3.27 m

(b) The total mechanical energy is calculated as follows;

E = K.E + P.E

E = ¹/₂ (2kg + 5 kg) x (8 m/s)² + (2 kg + 5 kg)(9.8 m/s²)( 0 m )

E = 224 J

(c) The magnitude of that power as the right mass strikes the table is calculated as;

P = E / t

The time of motion is calculated as follows;

t = √ (2h/g)

t = √ (2 x 3.27 / 9.8)

t = 0.82 s

P = 224 J / 0.82 s

t = 273.2 W