A weight lifter lifts a 200 kg barbell from the floor to a position directly over his head 2.5 meters. How much work did he do?
Work = force * distance
here force = mass times acceleration of gravity
distance is height difference, h
m g h
200 * 9.81 * 2.5
Joules if m in kg, g in meters/s^2 and h in meters
Well, if lifting weights was easy, they'd call it grocery shopping! To calculate the work done, we can use the formula: work = force × distance. In this case, the force is the weight of the barbell, which is 200 kg × 9.8 m/s² (acceleration due to gravity). So, the force is 1960 Newtons. The distance the lifter lifted the barbell is 2.5 meters. Now multiply 1960 N by 2.5 m and we get... drumroll please... 4900 joules of work! That's a whole lot of heavy lifting.
To calculate the work done by the weightlifter, we need to use the formula:
Work = Force x Distance
In this case, the force is the gravitational force acting on the barbell, and the distance is the height it was lifted.
The gravitational force can be calculated using the formula:
Force = mass x acceleration due to gravity
Given that the mass of the barbell is 200 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force:
Force = 200 kg x 9.8 m/s^2
Force = 1960 N
Now, we can calculate the work done:
Work = Force x Distance
Work = 1960 N x 2.5 m
Work = 4900 J
Therefore, the weightlifter did 4900 joules of work to lift the barbell.
To determine the amount of work done by the weight lifter, we need to use the formula:
Work (W) = Force (F) x Distance (d) x cos(θ),
where:
- Force (F) is the amount of force applied to lift the barbell,
- Distance (d) is the vertical distance over which the barbell is lifted,
- θ is the angle between the applied force and the direction of motion (in this case, it is 0°, as the force is vertical).
In this case, we are given:
- Force (F) = 200 kg (the weight of the barbell),
- Distance (d) = 2.5 meters.
Since the angle between the applied force and the direction of motion is 0°, cos(θ) becomes 1.
Now we can substitute the given values into the formula:
Work (W) = 200 kg x 2.5 meters x 1
= 500 Joules
Therefore, the weight lifter did 500 Joules of work in lifting the barbell.