The 4.01- kg weight that drives the time mechanism of a grandfather clock descends 21 cm in exactly 24 hours. What power is delivered to the mechanism?
P = F * d/t = mg * d/t
P = 4.01*9.8 * 0.21/24 = 0.3439 J/h =
9.6*10^-5 J/s.
To determine the power delivered to the mechanism of the grandfather clock, we can use the formula:
Power = Work / Time
Where:
Power is the rate at which work is done (measured in watts, W)
Work is the force applied to move the weight multiplied by the distance moved (measured in joules, J)
Time is the duration over which the work is done (measured in seconds, s)
First, let's calculate the work done by the weight:
Work = Force × Distance
The force can be calculated using Newton's second law of motion:
Force = mass × acceleration due to gravity
Given:
Mass of the weight (m) = 4.01 kg
Distance moved (d) = 21 cm = 0.21 m
Acceleration due to gravity (g) = 9.8 m/s^2
Calculating the force:
Force = m × g = 4.01 kg × 9.8 m/s^2 = 39.298 N
Now, we can calculate the work done:
Work = Force × Distance = 39.298 N × 0.21 m = 8.2522 J
Finally, we can calculate the power delivered to the mechanism:
Power = Work / Time
Given:
Time = 24 hours = 24 × 60 × 60 = 86,400 seconds
Calculating the power:
Power = 8.2522 J / 86,400 s = 0.0000955 W
Therefore, the power delivered to the mechanism of the grandfather clock is approximately 0.0000955 watts.
To calculate the power delivered to the mechanism of the grandfather clock, we need to use the formula:
Power = Work / Time
To find the work done by the weight, we can use the formula:
Work = Force x Distance
First, let's find the force exerted by the weight. We can use Newton's second law of motion, which states:
Force = mass x acceleration due to gravity
The mass of the weight is given as 4.01 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Force = 4.01 kg x 9.8 m/s^2
Force = 39.328 N
Now, let's find the distance the weight descends. It is given as 21 cm, which we need to convert to meters. Since 1 meter is equal to 100 centimeters, the distance is:
Distance = 21 cm / 100
Distance = 0.21 m
Now we can calculate the work done by the weight:
Work = Force x Distance
Work = 39.328 N x 0.21 m
Work = 8.25048 J (Joules)
Finally, we can find the power delivered to the mechanism by dividing the work done by the time taken. The time taken is given as 24 hours, which we need to convert to seconds:
Time = 24 hours x 60 minutes/hour x 60 seconds/minute
Time = 86,400 seconds
Power = Work / Time
Power = 8.25048 J / 86,400 s
Power ≈ 0.0000954 W (Watts)
Therefore, the power delivered to the mechanism of the grandfather clock is approximately 0.0000954 Watts.