Question

a crane lifts a 425 kg steel beam vertically upward a distance of 95 m. how much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s2? neglect frictional forces.

Answer 1

To calculate the work done by the crane on accelerating and lifting a 425 kg steel beam upwards 95 m, one must consider both the force due to gravity and the additional force required for upward acceleration, using the formula W = (mg + ma)d.

Step-by-step explanation:

The student's question is about calculating the work done by a crane lifting a steel beam, taking into account the upward acceleration of the beam. In physics, work is defined as the product of the force applied to an object and the distance over which the force is applied, in the direction of the force.

In this case, the work done by the crane involves two components:

• The work done against gravity.
• The work done to accelerate the beam upwards.

To find the total work done, we can use the formula:

W = (m × g + m × a) × d

Where:

• W is the work done by the crane (in joules).
• m is the mass of the beam (in kilograms).
• g is the acceleration due to gravity (9.8 m/s²).
• a is the upward acceleration of the beam (in m/s²).
• d is the distance the beam is lifted (in meters).

Plugging in the values provided:

W = (425 kg × 9.8 m/s² + 425 kg × 1.8 m/s²) × 95 m

W ≈ 72675 J

The crane would therefore do significant work lifting the steel beam.