A crane lifts an 425-kg object vertically upward a distance of 95 m. How much work (in kJ) does the crane do on object if object accelerates upward at 1.8 m/s2? Neglect frictional forces. How much work (in kJ) does gravity do on the object if object accelerates upward at 1.8 m/s2? Neglect frictional forces.
F = ma
work = force * distance
To calculate the work done by the crane on the object, we need to use the formula:
Work = Force × Distance
The force can be calculated using Newton's second law of motion, which states that Force (F) = mass (m) × acceleration (a).
Given:
Mass (m) = 425 kg
Acceleration (a) = 1.8 m/s²
Distance (d) = 95 m
First, let's calculate the force exerted by the crane on the object:
Force (F) = m × a = 425 kg × 1.8 m/s² = 765 N
Now, we can calculate the work done by the crane using the force and distance:
Work = F × d = 765 N × 95 m
To convert the units to kJ, we need to divide the result by 1000:
Work = (765 N × 95 m) ÷ 1000 = 72775 J ÷ 1000 = 72.775 kJ
Therefore, the crane does 72.775 kJ of work on the object.
Next, let's calculate the work done by gravity on the object. Since the object is being lifted vertically upward, the force of gravity is opposite to the direction of motion, so the work done is negative.
The work done by gravity can be calculated using the formula:
Work = Force of gravity × Distance
The force of gravity can be calculated using the formula: Force of gravity (Fg) = m × g, where g is the acceleration due to gravity (approximately 9.8 m/s²).
Force of gravity (Fg) = 425 kg × 9.8 m/s² = 4165 N
Now, we can calculate the work done by gravity using the force of gravity and distance:
Work = Fg × d = 4165 N × 95 m
Again, to convert the units to kJ, we need to divide the result by 1000:
Work = (4165 N × 95 m) ÷ 1000 = 395675 J ÷ 1000 = 395.675 kJ
Therefore, gravity does 395.675 kJ of work on the object, in the opposite direction of its motion.