Final answer:
The work done on a 250 kg block by the gravitational force as it slides down a 40 m incline at a 30° angle is 49,000 Joules.
Step-by-step explanation:
The work done on a block by the gravitational force as it slides down an incline can be found using the work-energy principle. For a block of mass 250 kg sliding down an incline that makes a 30° angle with the horizontal, the work done by gravity Wg is the component of the gravitational force along the incline times the distance traveled along the incline.
The gravitational force acting on the block is mg, where m is the mass and g is the acceleration due to gravity. The component of this force along the incline is mg sin(θ), where θ is the incline angle. Therefore, the work done by gravity is:
Wg = mg sin(θ) d
Plugging in the values, we have:
Wg = (250 kg)(9.8 m/s2) sin(30°) (40 m)
Wg = (250 kg)(9.8 m/s2)(0.5)(40 m)
Wg = 49,000 J
Therefore, the work done on the object by gravitational force is 49,000 Joules.