A 150 kg safe on frictionless casters is to be raised with 1.2 meters off the ground to the bed of a truck. Planks 4m long are available for the safe to be rolled along. How much force is needed to push the safe up the truck?
MA=4/1.2
force=150*9.8*4/1.2
MA=4/1.2
force=150*9.8*1.2/4
To calculate the force needed to push the safe up the truck, we need to consider the work done against gravity.
The work done (W) against gravity is given by the formula: W = m * g * h
Where:
m = mass of the safe (150 kg)
g = acceleration due to gravity (9.8 m/s²)
h = height the safe is lifted (1.2 m)
Plugging the values into the formula, we get:
W = 150 kg * 9.8 m/s² * 1.2 m
Calculating this, we find:
W = 1764 Joules
The work done is equal to the force (F) applied multiplied by the distance (d) over which it is applied. In this case, the distance is the length of the plank (4 m).
Therefore, F * 4 m = 1764 J
Rearranging the formula, we have:
F = 1764 J / 4 m
Calculating this, we find:
F = 441 Newtons
Therefore, approximately 441 Newtons of force are needed to push the safe up the truck.
To determine the amount of force needed to push the safe up the truck, we need to consider the work done and the distance over which the force is applied.
The work done is given by the formula:
Work = Force × Distance
The force required to raise an object against gravity is equal to its weight, which can be calculated using the formula:
Weight = mass × gravitational acceleration
In this case, the gravitational acceleration is standard 9.8 m/s^2.
Since the safe is raised vertically, the distance over which the force is applied is the vertical distance the safe is lifted, which is 1.2 meters.
Let's calculate the weight of the safe:
Weight = mass × gravitational acceleration
Weight = 150 kg × 9.8 m/s^2
Weight = 1470 N
Now, let's calculate the work done:
Work = Force × Distance
Work = Weight × Distance
Work = 1470 N × 1.2 m
Work = 1764 joules
The force required to push the safe up the truck equals the work done divided by the distance. In this case, the distance is the length of the plank, which is 4 meters.
Force = Work ÷ Distance
Force = 1764 J ÷ 4 m
Force = 441 N
Therefore, a force of 441 Newtons is needed to push the safe up the truck.