if 2.0 J of work is done in raising a 180 g apple, how far is it lifted? equation used to figure this problem out?
PE gained=work applied
mgh=2.0J
180 g = .180 kg
Force = m g = .180 * 9.81 Newtons
work = Force * distance
so
distance in meters = 2 Joules / (.180*9.81)Newtons
To determine the height the apple is lifted, we can use the equation for work:
Work = Force × Distance × cos(θ),
where Work is given as 2.0 J (joules), Force is the force applied to lift the apple, Distance is the height the apple is lifted, and θ is the angle between the direction of the force and the direction of motion (which is 0° since the force is acting vertically).
First, we need to find the force applied to lift the apple. The force can be calculated using the equation:
Force = mass × acceleration due to gravity,
where mass is given as 180 g and acceleration due to gravity is approximately 9.8 m/s^2.
Converting the mass to kilograms:
180 g = 0.18 kg (1 g = 0.001 kg).
Now, let's calculate the force:
Force = 0.18 kg × 9.8 m/s^2 = 1.764 N.
Now that we have the force, we can rearrange the equation for work to solve for distance:
Distance = Work / (Force × cos(θ)).
Since θ = 0° (cos(0°) = 1), the equation simplifies to:
Distance = Work / Force.
Plugging in the values:
Distance = 2.0 J / 1.764 N ≈ 1.134 m.
Therefore, the apple is lifted approximately 1.134 meters.