a cord is used to lower vertically a block of mass M a distance d at a constant downward acceleration of 1\4 g, find the work done by the cord on the block ? FIND THE WORK DONE BY THE FORCE OF GRAVITT
force of gravity does M*g*d work.
To find the work done by the cord on the block and the work done by the force of gravity, we need to understand the definition of work. Work is given by the equation:
Work = Force * Distance * cos(theta),
where Force is the applied force, Distance is the displacement due to the force, and theta is the angle between the direction of the applied force and the displacement.
In this case, the block is being lowered vertically, so the angle between the force and displacement is 0 degrees, and cos(0) = 1. Therefore, the equation simplifies to:
Work = Force * Distance.
Let's calculate the work done by the cord first.
The downward acceleration of the block is 1/4 g, where g is the acceleration due to gravity.
Force = Mass * Acceleration = M * (1/4 g).
The block is lowered vertically a distance d, so the Distance = d.
Therefore, the work done by the cord on the block is:
Work done by the cord = Force * Distance = M * (1/4 g) * d.
Now, let's calculate the work done by the force of gravity.
The force of gravity acting on the block is given by:
Force of gravity = Mass * Acceleration due to gravity = M * g.
The distance d is vertically downwards, so the angle between the force of gravity and the displacement is 0 degrees, and cos(0) = 1. Therefore, the work done by the force of gravity is:
Work done by the force of gravity = Force of gravity * Distance = M * g * d.
In summary:
- The work done by the cord on the block is M * (1/4 g) * d.
- The work done by the force of gravity is M * g * d.