How much work is done by the gravitational force on an object of mass 9.40 kg that is initially at rest when it falls down for a time of 1.85 seconds. Ignore air resistance
To calculate the work done by the gravitational force, we need to use the formula:
Work = Force x Displacement x cos(theta)
In this case, the force is the weight of the object, which is given by:
Force = mass x acceleration due to gravity
The displacement is the vertical distance traveled by the object during the fall. Since the object is initially at rest, we can use the equation of motion:
Displacement = (1/2) x acceleration x time^2
Given:
mass = 9.40 kg
time = 1.85 seconds
acceleration due to gravity = 9.8 m/s^2
Let's calculate each component step by step:
1. Calculate the force:
Force = mass x acceleration due to gravity
Force = 9.40 kg x 9.8 m/s^2
Force = 92.12 N
2. Calculate the displacement:
Displacement = (1/2) x acceleration x time^2
Displacement = (1/2) x 9.8 m/s^2 x (1.85 s)^2
Displacement = 16.11 m
3. Calculate the angle between the force and displacement vectors. In this case, the angle is 0 degrees because the force and displacement are parallel.
4. Calculate the work:
Work = Force x Displacement x cos(theta)
Work = 92.12 N x 16.11 m x cos(0°)
Work = 1485.95 J
Therefore, the work done by the gravitational force on the object is 1485.95 Joules (J).