A 4.0 kg object is lifted 1.5 m. (a) how much work is done against the earth's gravity ? (b) repeat if the object is lowered insteadof lifted
-58.86J
F=mg
m=4kg
g=9.81
W=Fxd
W=4(9.81)(1.5)
=58.86 or 59 J
To find the amount of work done against the Earth's gravity, we can use the formula:
Work = Force × Distance × cos(θ)
where:
- Force is the weight of the object, which is the product of its mass (m) and acceleration due to gravity (g).
- Distance is the height through which the object is lifted or lowered.
- θ is the angle between the force vector and the direction of displacement.
Let's calculate the work done for both scenarios.
(a) When the object is lifted:
Weight = mass × acceleration due to gravity = 4.0 kg × 9.8 m/s² ≈ 39.2 N
Distance = 1.5 m
θ = 0° (since the force and displacement are in the same direction)
Work = 39.2 N × 1.5 m × cos(0°)
Work = 39.2 N × 1.5 m × 1
Work = 58.8 joules
Therefore, 58.8 joules of work is done against the Earth's gravity when the object is lifted.
(b) When the object is lowered:
In this case, the force and displacement are in opposite directions, so the angle θ is 180°.
Work = 39.2 N × 1.5 m × cos(180°)
Since cos(180°) = -1, the negative sign indicates that the work is done by the Earth's gravity, not against it.
Work = 39.2 N × 1.5 m × (-1)
Work = -58.8 joules
Therefore, when the object is lowered, the work done against the Earth's gravity is -58.8 joules, indicating that the Earth's gravity is doing the work.
The definition of work is (force) x (distance moved in the direction of the force)
(a) In this case, the force is M*g.
I assume that you know the value of g.
M is the mass. Complete the calculation.
(b) Change the sign of the previous answer. Negative work is done by whatever is lowering the weight.
Force X Displacement
Force=mass X gravity
=> m g s
= 4 x 10 x -1.5
= -60 J