A ball of mass 35kg runs up a flight of 30steps an approximate height of 10cm .
If this entire movement was done on 20seconds . Calculate to two decimal places,the power of the ball
First, we need to calculate the total work done by the ball.
Work = Force x Distance
Gravity is the force acting on the ball and the distance it was moved is equal to the height of the steps.
Work = mgh
where m is the mass of the ball, g is the acceleration due to gravity (9.81 m/s²), and h is the height of the steps (0.1 m).
Work = 35 kg x 9.81 m/s² x 0.1 m = 34.335 J
Next, we can calculate the power of the ball using the formula:
Power = Work / Time
where time is given as 20 seconds.
Power = 34.335 J / 20 s = 1.71675 W
Rounding to two decimal places, the power of the ball is approximately 1.72 W.
To calculate the power of the ball, we can use the formula:
Power = Work / Time
First, let's calculate the work done by the ball.
Work = force * distance
The force exerted by the ball is equal to its weight, which is given by:
Force = mass * acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s².
Force = 35 kg * 9.8 m/s²
Now, let's calculate the distance traveled by the ball. The total height is 10 cm, but we need to convert it to meters:
Distance = total height * number of steps
Total height = 10 cm = 0.1 m
Number of steps = 30
Distance = 0.1 m * 30
Next, we can plug these values into the formula for work:
Work = Force * Distance
Finally, we can calculate the power using the formula:
Power = Work / Time
Now let's calculate the values step-by-step:
Force = 35 kg * 9.8 m/s²
Force = 343 N (to 2 decimal places)
Distance = 0.1 m * 30
Distance = 3 m
Work = 343 N * 3 m
Work = 1029 J (to 2 decimal places)
Power = Work / Time
Power = 1029 J / 20 s
Power = 51.45 W (to 2 decimal places)
Therefore, the power of the ball is approximately 51.45 Watts.