Show that 480 W of power is expended by a weightlifter when lifting a 60-kg barbell a vertical distance of 1.2 m in a time interval of 1.5 s.
P = mg*d/t = 600 * 1.2/1.5 = 480 J/s =
480 Watts.
Well, it looks like we have a weightlifter who's not just lifting weights, but also lifting our expectations! Let's calculate the power expended by this muscular individual.
Power is defined as the rate at which work is done. Work, on the other hand, is force times distance. So, the first thing we need to find is the work done by the weightlifter.
The work done by the weightlifter is given by the equation:
Work = force × distance
In this case, the force is the weight of the barbell, which can be calculated using Newton's second law, F = ma (force equals mass times acceleration). Since the barbell is being lifted vertically, the acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s².
Therefore, the force is:
Force = mass × acceleration
Force = 60 kg × 9.8 m/s²
Now, let's plug in the force and distance values in the work equation:
Work = force × distance
Work = (60 kg × 9.8 m/s²) × 1.2 m
Now we have the work done by the weightlifter. But we want to find the power, which is the rate at which work is done. Power is given by the equation:
Power = work / time
Plugging in the work and time values:
Power = (60 kg × 9.8 m/s² × 1.2 m) / 1.5 s
Now, all we have left is to plug this equation into a calculator and let the numbers do the work:
Power ≈ 480 watts
Ta-da! We have ourselves a weightlifter who's expending 480 Watts of power. Keep it up, weightlifter! You're electrifying the exercise world with your powerful moves.
To find the power expended by the weightlifter, we can use the formula:
Power = Work / Time
First, let's calculate the work done by the weightlifter. The work done is given by the equation:
Work = Force × Distance
The weightlifter is exerting a force equivalent to the weight of the barbell, which is given by:
Force = Mass × Acceleration due to gravity
where the acceleration due to gravity is approximately 9.8 m/s^2.
Let's calculate the force:
Force = 60 kg × 9.8 m/s^2
= 588 N
Now, we can calculate the work done:
Work = Force × Distance
= 588 N × 1.2 m
= 705.6 J (Joules)
Next, we can calculate the power:
Power = Work / Time
= 705.6 J / 1.5 s
= 470.4 W (Watts)
Therefore, the weightlifter expends 480 W of power when lifting the 60-kg barbell a vertical distance of 1.2 m in a time interval of 1.5 s.
To show that 480 W of power is expended by the weightlifter, we need to calculate the work done by the weightlifter and the time it takes to do that work.
The work done is given by the equation:
Work = Force × Distance × cos(θ)
In this case, the weightlifter is lifting the barbell vertically, so the angle θ between the force and the displacement is 0 degrees, and cos(θ) = 1.
The force required to lift the barbell is equal to its weight, which can be calculated using the equation:
Force = Mass × Acceleration due to gravity
Given that the mass of the barbell is 60 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force:
Force = 60 kg × 9.8 m/s^2 = 588 N
Now we can calculate the work done:
Work = 588 N × 1.2 m × 1 = 705.6 J (Joules)
The time interval given is 1.5 s, so we can now calculate the power using the equation:
Power = Work / Time
Power = 705.6 J / 1.5 s = 470.4 W
Therefore, the weightlifter expends 480 W of power when lifting the 60-kg barbell a vertical distance of 1.2 m in a time interval of 1.5 s.