An elephant applies a force of 5000 N through a rope on a bundle of wood logs and moves them through a displacement of 250 m. The rope makes an angle of 28 degrees with the horizontal ground.
a. calculate the work done by the elephant in moving the load
b. If the elephant moved the load in a time of 1/2 hour, calculate the power output by the elephant in watts AND horsepower
work=F*d * cosTheta=5000*250*cos28
power(watts)=work/timeInSeconds
power(hp)=power(watts)/546
To calculate the work done by the elephant in moving the load, we can use the formula:
Work = Force * Distance * cos(theta)
where:
- Force is the applied force by the elephant (5000 N)
- Distance is the displacement of the bundle of wood logs (250 m)
- theta is the angle between the force and the displacement (28 degrees)
a. Calculate the work done by the elephant:
Work = 5000 N * 250 m * cos(28 degrees)
To find the cosine of 28 degrees, you can use a scientific calculator or an online calculator. The cosine of 28 degrees is approximately 0.8829.
Work = 5000 N * 250 m * 0.8829
Work = 1,103,625 Joules (rounded to the nearest whole number)
Therefore, the work done by the elephant in moving the load is approximately 1,103,625 Joules.
b. To calculate the power output by the elephant, we can use the formula:
Power = Work / Time
where:
- Work is the work done by the elephant (1,103,625 Joules)
- Time is the time taken to move the load (1/2 hour)
However, before calculating the power in watts and horsepower, we need to convert the time from hours to seconds.
1/2 hour = 0.5 * 60 * 60 seconds
= 1800 seconds
Now, calculate the power in watts:
Power (watts) = 1,103,625 Joules / 1800 seconds
= 613.125 watts (rounded to three decimal places)
To convert the power from watts to horsepower, we can use the conversion factor:
1 horsepower = 746 watts
Power (horsepower) = 613.125 watts / 746
= 0.822 horsepower (rounded to three decimal places)
Therefore, the power output by the elephant is approximately 613.125 watts or 0.822 horsepower.