A 45.4 kg of beer rolls down a 3.05 m long plank leading from the flatbed of a truck 0.880 m above the ground. Determine the amount of work (in Joules) done on the keg by gravity.
what is mg*height
Gravitational potential energy.
GPE of one, with respect to the other being at zero PE:
GPE= -Gm/r
To determine the amount of work done on the keg by gravity, we need to use the equation:
Work = Force × Distance × cosθ
In this case, the force is the weight of the keg, the distance is the length of the plank, and θ is the angle between the force vector and the direction of motion.
First, let's calculate the weight of the keg using the formula:
Weight = mass × gravity
where the mass is given as 45.4 kg and gravity is approximately 9.8 m/s²:
Weight = 45.4 kg × 9.8 m/s² = 445.92 N
Next, we need to find the angle θ. Since the plank is inclined, the force vector is perpendicular to the plank, and the direction of motion is parallel to the plank. Therefore, θ is the angle between the vertical force vector and the direction of motion, which is the angle of the incline.
We can use trigonometry to find this angle. The height of the plank (0.880 m) and the length of the plank (3.05 m) form a right triangle. So, the tangent of the angle is the ratio of the height to the length:
tanθ = height / length
tanθ = 0.880 m / 3.05 m
Using a scientific calculator or trigonometric table, we can find the inverse tangent (arctan) of this value to determine the angle θ:
θ = arctan (0.880 m / 3.05 m)
Computing this value will give us θ = 16.145°.
Now we can substitute the values into the work equation:
Work = 445.92 N × 3.05 m × cos(16.145°)
Finally, calculating the value will give us the amount of work done on the keg by gravity, expressed in Joules.