A 150kg safe on a frictionless casters is to be raised 1.20 m off the ground to the bed of a truck. Planks 3.0 m long are available for the safe to be rolled along. How much force is needed to push the safe up to the truck
Force x (plank length), which is the work done, must equal the increase in potential energy: (mass) x g * (height raised)
F * 3.0 = 150 x 9.81 x 1.20
Solve for F, which will be in Newtons
588
To determine the force needed to push the safe up to the truck, we need to consider the work-energy principle. The work done to raise the safe is equal to its change in potential energy. The formula for calculating work is:
Work = Force × Distance
The potential energy of an object is given by:
Potential Energy = Mass × Gravitational Acceleration × Height
In this case, the height is 1.20 m, and the mass of the safe is 150 kg. The gravitational acceleration is approximately 9.8 m/s². Plugging these values into the potential energy equation, we get:
Potential Energy = 150 kg × 9.8 m/s² × 1.20 m
Next, we need to calculate the distance over which the force needs to be applied. Since planks 3.0 m long are available, we can assume that the force needs to be applied over a distance of 3.0 m.
Now, we know the potential energy and distance. By rearranging the work formula, we can solve for force:
Force = Work / Distance
Force = (Potential Energy) / (Distance)
Force = (150 kg × 9.8 m/s² × 1.20 m) / 3.0 m
Calculating this expression will give us the force needed to push the safe up to the truck.