Question

2. Bank robbers have pushed a 1000 kg safe to a second story floor-to-ceiling window. They plan to break the window, then lower the safe 3.0 m to their truck. They stack up 500 kg of furniture, tie a rope between the rope and the furniture, and then place the rope over a pulley. Then they push the safe out of the window. What is the safe speed when it hits the truck

Answer 1

5.4 m/s

Step-by-step explanation:

Given that

Mass of the safe, m1 = 1000 kg

Distance to lower the safe, d = 3 m

Mass of furniture, m2 = 500 kg.

Speed of the safe, v = ?

To get the final speed by the time that the safe hits the truck, we first find its acceleration.

The total mass of the system is M = 1000 + 500 kg = 1500 kg

One of the forces acting on the system is that of gravity, and it acts on the safe friction acting on the furniture. Using the formula, we have

= m1*g - mu*m2g

= 1000 * 9.81 - 0.5 * 500 * 9.81

= 7357.5 N

From this calculated weight, we find the acceleration.

Acceleration, a = F/m

Acceleration, a = 7357.5 / 1500

Acceleration, a = 4.905 m/s²

From the question, we know that the Initial speed = 0 m/s

So, employing the use of one of the equations of motion, we have

v² - u² = 2aS

v² - 0 = 2 * 4.905 * 3

v² = 29.43

v = √29.43

v = 5.4 m/s