Question

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 meteres to their truck. Not being too clever, they stack up 500 kg of furnature, tie a rope between the safe and the furnature, and place the rope over the pully. Then they push the safe out of the window. what is the saves speed when it hits the truck?

Answer 1

The safe's speed when it hits the truck is approximately 7.67 m/s, determined by converting the safe's initial potential energy to kinetic energy and solving for velocity.

Step-by-step explanation:

The question is asking to calculate the safe's speed when it hits the truck, considering it's being lowered from a second-story window with the help of a pulley system. To find the safe's speed, we can use the principle of conservation of energy, where the potential energy of the safe at the beginning will be converted to kinetic energy just before it hits the truck.

Initial potential energy (PEinitial) of the safe can be calculated using the formula PE = mgh, where m is the mass (1000 kg for the safe), g is the acceleration due to gravity (9.8 m/s2), and h is the height (3.0 meters). The kinetic energy (KE) of the safe when it hits the truck can be represented as KE = 1/2mv2, where v is the final velocity that we're solving for.

Setting the initial potential energy equal to the final kinetic energy (PEinitial = KE), and solving for v, we get:

1000 kg × 9.8 m/s2 × 3.0 m = 1/2 × 1000 kg × v2

29400 J = 500 kg × v2

v2 = 58.8 m2/s2

v = √58.8 m2/s2 ≈ 7.67 m/s

Therefore, the safe's speed when it hits the truck is approximately 7.67 m/s.