If a man pushes pushes a drum of oil of 10 kg up and incline OA, if OA is 5m and AB is 3m.
What work is done by the man?
What work is done if the drum is just lifted from b to a??
If it goes up 3 meters
then the gain in potential energy is m g h = 10 * 9.81 (on earth) * 3 Joules
Either way that is the amount of work done if no energy is lost to friction or radiation or whatever.
Now if you did not realize that the you would figure
the Force exerted by the man is m g sin( incline angle
= m g (3/5)
and he pushed for 5 meters
so
m g * (3/5) = 5 = m g * 3 = m g h like we said before
typos
m g * (3/5) * 5 = m g * 3 = m g h like we said before
To calculate the work done in both scenarios, we need to understand the concept of work and use the formula for work.
Work is defined as the product of the force applied to an object and the displacement of that object in the direction of the force. Mathematically, work (W) is given by the equation:
W = F * d * cos(theta)
where F is the force applied, d is the displacement of the object, and theta is the angle between the force and the displacement vectors.
Now, let's calculate the work done in each scenario:
1. When the man pushes the drum up the incline OA:
- The force acting on the drum is the force applied by the man.
- The displacement is the distance along the incline.
- The angle between the force and displacement vectors is 0 degrees since they are parallel.
- Substituting these values into the formula, we get:
W = F * d * cos(0 degrees) = F * d
- Since we only have the mass of the drum (10 kg) but not the force he applies, we can use the gravitational force to calculate the force applied.
- The weight of the drum (force applied) is given by:
F = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
- Substituting the values, we get:
F = 10 kg * 9.8 m/s^2 = 98 N (approximately)
- The displacement along the incline OA is 5 m.
- Calculating the work:
W = F * d = 98 N * 5 m = 490 J (Joules)
2. When the drum is just lifted from B to A (vertically):
- In this case, the force applied is the same, i.e., the weight of the drum, which is 98 N.
- The displacement is the vertical distance from B to A, which is 3 m.
- The angle between the force and displacement vectors is 90 degrees since they are perpendicular.
- Calculating the work using the formula:
W = F * d * cos(90 degrees) = F * d * 0
- Because cos(90 degrees) is 0, the work done in this scenario is zero (0 J).
Therefore, the work done by the man when pushing the drum up the incline OA is 490 Joules, and the work done when the drum is lifted vertically from B to A is zero Joules.