A crane lifts a 425-kg steel beam vertically upward a distance of 95 m. How much work (in kJ) does gravity do on the beam if the beam accelerates upward at 1.8 m/s2? Neglect frictional forces. Give your answer to 3 significant figures and remember that work can be positive or negative.
the gravitational force is constant over this short distance
the change in gravitational potential energy (work) is ... m * g * h
... the work is negative (against gravity)
FYI ... technically, the answer sig fig is the smallest of the input data
... the distance (h) is only two sig fig
To calculate the work done by gravity on the steel beam, we need to use the formula:
Work = Force × Distance
First, we need to find the force exerted by gravity on the beam.
The force exerted by gravity can be calculated using the equation:
Force = mass × acceleration due to gravity
Given:
mass of the steel beam (m) = 425 kg
acceleration due to gravity (g) = 9.8 m/s² (approximate value on Earth)
Substituting these values into the equation, we get:
Force = 425 kg × 9.8 m/s² = 4165 N (approximately)
Next, we need to calculate the distance over which the force is exerted.
Given:
distance (d) = 95 m
Now we can substitute the force and distance values into the work formula:
Work = Force × Distance
Work = 4165 N × 95 m = 395,675 N·m
Since we need the answer in kilojoules (kJ), we need to convert the unit of work from newton-meters (N·m) to kilojoules (kJ).
1 kilojoule (kJ) = 1000 joules (J)
Converting the unit, we get:
Work = 395,675 N·m × (1 kJ / 1000 J) = 395.675 kJ
Therefore, the work done by gravity on the beam is approximately 395.675 kJ.
To calculate the work done by gravity on the beam, we can use the equation:
Work = force × distance
The force exerted by gravity on the beam is given by the equation:
Force = mass × acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2, but since the beam is accelerating upward at 1.8 m/s^2, we need to subtract this value from the acceleration due to gravity. Thus, the net acceleration due to gravity is 9.8 - 1.8 = 8 m/s^2.
Now, we can calculate the force exerted by gravity:
Force = mass × acceleration due to gravity
= 425 kg × 8 m/s^2
= 3400 N
Next, we can calculate the work done by gravity using the equation:
Work = force × distance
= 3400 N × 95 m
= 323000 J
Finally, we can convert the work from joules to kilojoules:
Work = 323000 J / 1000
= 323 kJ
Therefore, the work done by gravity on the beam is 323 kJ.