A cable pulls a crate of mass 19.0 kg across the floor in 6.8 s. If the total distance traveled is 5.40 m, find the power used by the cable.
w=md
186.2(5.40)
w= 1005.48
p=w/t
p=1005.48/5.40
answer: 147.9 W
To find the power used by the cable, we need to calculate the work done first. The work done is given by the formula:
W = force × distance
In this case, the force is the tension in the cable, and the distance is the total distance traveled by the crate. However, we don't have the tension in the cable given directly. Instead, we can use Newton's second law to find the tension.
The force applied by the cable is equal to the mass of the crate multiplied by its acceleration:
Force = mass × acceleration
Since the crate is being pulled across the floor, its acceleration can be calculated using the equation of motion:
acceleration = (final velocity - initial velocity) / time
Here, the final velocity is the velocity of the crate at the end of the 6.8 second interval, and the initial velocity is 0 (assuming the crate starts from rest).
Now we can calculate the acceleration:
acceleration = (final velocity - 0) / 6.8 = final velocity / 6.8
Since we don't have the final velocity, we need to find it. We can use another equation of motion to find the final velocity:
final velocity² = initial velocity² + 2 × acceleration × distance
The initial velocity is 0, so this simplifies to:
final velocity² = 2 × acceleration × distance
We can rearrange this equation to solve for the final velocity:
final velocity = sqrt(2 × acceleration × distance)
Now that we have the final velocity, we can calculate the acceleration:
acceleration = final velocity / 6.8
Finally, we can calculate the force:
Force = mass × acceleration
Now that we have the force, we can calculate the work done:
Work = Force × distance
Finally, to find the power used by the cable, we use the formula:
Power = Work / time
Now we can substitute the given values and calculate the power:
Mass of the crate = 19.0 kg
Distance traveled = 5.40 m
Time = 6.8 s
1. Calculate the acceleration:
acceleration = sqrt(2 × acceleration × distance) / 6.8
2. Calculate the force:
Force = mass × acceleration
3. Calculate the work done:
Work = Force × distance
4. Calculate the power:
Power = Work / time
After performing the calculations, the power used by the cable is 147.9 W (rounded to one decimal place).