The two blocks are connected by a light

string that passes over a frictionless pulley with a negligible mass. The 3 kg block lies on a rough horizontal surface with a constant coefficient of kinetic friction 0:3. The hanging block has a mass of 8 kg. The system starts from rest. The acceleration of gravity is 9.8 What is the speed of the 8 kg hanging mass when it has fallen a height 8 m? Answer in
units of m/s.

daaang, I am glad I am not in your class.
I would be the dumb blonde there xD
Goodluck and best wishes!

No worries! I'm here to help you understand. Let's break down the problem step by step.

First, let's calculate the gravitational potential energy (PE) of the hanging block. The formula for gravitational potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

Given:
Mass of the hanging block (m) = 8 kg
Acceleration due to gravity (g) = 9.8 m/s²
Height (h) = 8 m

PE = 8 kg * 9.8 m/s² * 8 m
PE = 627.2 J (joules)

Next, let's determine the work done by friction as the block falls. The work done by friction can be calculated using the formula W = F_friction * d, where F_friction is the force of friction and d is the distance.

The force of friction (F_friction) can be calculated using the formula F_friction = μ * N, where μ is the coefficient of kinetic friction and N is the normal force. The normal force is equal to the weight of the block, which is given by m * g.

Given:
Mass of the block on the surface (m) = 3 kg
Coefficient of kinetic friction (μ) = 0.3
Acceleration due to gravity (g) = 9.8 m/s²
Distance (d) = 8 m

First, calculate the normal force:
N = m * g
N = 3 kg * 9.8 m/s²
N = 29.4 N

Next, calculate the force of friction:
F_friction = μ * N
F_friction = 0.3 * 29.4 N
F_friction = 8.82 N

Now, calculate the work done by friction:
W = F_friction * d
W = 8.82 N * 8 m
W = 70.56 J (joules)

Next, let's calculate the change in kinetic energy (KE) of the hanging block, which is equal to the work done by the friction force:
ΔKE = W = 70.56 J

Since the system starts from rest, the change in kinetic energy is equal to the final kinetic energy (KE) of the hanging block. Thus, ΔKE = KE = 70.56 J.

Finally, we can calculate the final velocity (v) of the hanging block using the formula KE = 0.5 * m * v², where m is the mass and v is the velocity.

Given:
Mass of the hanging block (m) = 8 kg
Final kinetic energy (KE) = 70.56 J

Rearranging the formula, we get:
v² = (2 * KE) / m
v² = (2 * 70.56 J) / 8 kg
v² = 17.64 J / 8 kg
v² = 2.205 m²/s²

Taking the square root of both sides, we find:
v = √(2.205 m²/s²)
v ≈ 1.486 m/s

Therefore, the speed of the 8 kg hanging mass when it has fallen a height of 8 m is approximately 1.486 m/s.