A body of mass 10kg is to be raise from the bottom to the top of an inclined plane 5m long and 3.0m off the ground at the top assuming a frictionless surface,how much work must be done by the force parallel to the plane pushing the block up to a constant speed?
whether it is slid up or lifted up , the work is equal to the change in gravitational potential energy ... m g h
To find the work done in raising the body up the inclined plane, we need to consider the gravitational force and the displacement of the body.
First, we calculate the gravitational potential energy of the body at the bottom and top of the inclined plane using the formula:
Potential Energy = mass x height x gravity
At the bottom of the inclined plane:
Potential Energy (bottom) = 10 kg x 0 m x 9.8 m/s² = 0 J
At the top of the inclined plane:
Potential Energy (top) = 10 kg x 3.0 m x 9.8 m/s² = 294 J
The work done by the force parallel to the plane pushing the block up to a constant speed is equal to the change in potential energy.
Work = Potential Energy (top) - Potential Energy (bottom)
Work = 294 J - 0 J
Work = 294 J
Therefore, the work done by the force parallel to the plane in pushing the block up to a constant speed is 294 Joules.
To calculate the work done to raise the body up the inclined plane, we need to use the formula for work:
Work = Force × Distance × cos θ
Where:
Force is the component of force parallel to the plane,
Distance is the displacement along the inclined plane, and
θ is the angle between the force and the direction of the displacement.
In this case, the displacement along the plane is 5m, and since the force is parallel to the plane and pushing the block up to a constant speed, the angle θ between the force and the direction of displacement is zero degrees.
Given that there is no friction, the force required to push the block up the incline is equal to the component of the gravitational force acting parallel to the incline. This component is calculated as:
Force = mass × acceleration due to gravity × sin θ
Since the force parallel to the plane is opposing the gravitational force, we can use the negative sign:
Force = - (mass × acceleration due to gravity × sin θ)
In this case, the mass is 10 kg, and the acceleration due to gravity is 9.8 m/s^2. Since the angle θ is zero degrees, the sin θ becomes zero:
Force = - (10 kg × 9.8 m/s^2 × sin 0°)
Simplifying further:
Force = - (10 kg × 9.8 m/s^2 × 0)
Since sin 0° equals zero, the force required to push the block up the incline is zero.
In conclusion, no work needs to be done by the force parallel to the plane to push the block up to a constant speed.