A pulley system has an efficiency of 87.5%. How much rope must be pulled if a force of 648N is needed to lift a 105 kg desk 2.46m?
work done on desk = m g h = 105 * 9.81 * 2.46 = 2534 Joules
so work in = 2534 / 0.875 = 2896 Joules
that is your 648 times distance your hand moved holding the rope
2896 = 648 * x
4.47 meters
I think maybe a typo, 648 N is too big, maybe 64.8 ? Any block and tackle system does better than that.
Well, let's not "rope" our way around this question! To determine how much rope must be pulled, we can first calculate the work done against gravity using the given force and distance.
Work = force × distance
Work = 648N × 2.46m
Now, since the efficiency of the pulley system is 87.5%, only 87.5% of the calculated work is actually done. So, we need to find out how much work is required overall, with the given efficiency.
Overall work = (Work / Efficiency)
Overall work = (648N × 2.46m) / (87.5%)
Now, we know that work is also equal to force × distance, so we can rearrange the formula to solve for force.
Overall work = force × distance
force = Overall work / distance
Using this formula, we can calculate the force required with the given work and distance.
force = (Overall work / distance)
force = (648N × 2.46m) / (87.5%)
After calculating the force required, you'll have an approximate value of how much force is required. Keep in mind that the actual amount of rope you need to pull may vary slightly due to other factors like friction and energy losses. But hey, at least now you have a rough estimate to get started with your desk-lifting endeavor!
To calculate the length of rope that needs to be pulled, we can start by finding the work done in lifting the desk. The work is given by the equation:
Work = force * distance
In this case, the force required is 648N and the distance is 2.46m. Therefore, the work done is:
Work = 648N * 2.46m = 1593.6 Joules
Now, we need to account for the efficiency of the pulley system. Efficiency is defined as the ratio of useful work output to the work input, expressed as a percentage. In this case, the efficiency is 87.5%.
Efficiency = (useful work output / work input) * 100%
Rearranging the equation, we can solve for the work input:
work input = (useful work output / efficiency) * 100%
Substituting the values we have:
work input = (1593.6 Joules / 87.5%) * 100% = 1820.114 Joules
Finally, we can use the equation for work done to find the length of rope that needs to be pulled (L) using the formula:
Work = force * distance
Rearranging the equation, we have:
distance = work / force
Substituting the values we have:
distance = 1820.114 Joules / 648N = 2.812m
Therefore, approximately 2.812 meters of rope must be pulled to lift the 105 kg desk using a force of 648N with an efficiency of 87.5%.
To determine how much rope must be pulled to lift the desk, we first need to calculate the work done to lift the desk. The formula for work is:
Work (W) = Force (F) * Distance (d) * cos(theta)
In this case, the force (F) is given as 648N, and the distance (d) is given as 2.46m. Since the angle (theta) is not provided, we can assume it to be zero degrees, which means cos(theta) is equal to 1.
Therefore, the work done to lift the desk is:
W = 648N * 2.46m * 1
W = 1593.12 Joules
Now, the efficiency of the pulley system is given as 87.5%. Efficiency is defined as the ratio of useful work output to the total work input. In this case, the useful work output is the work done to lift the desk (1593.12 Joules).
Therefore, we can calculate the total work input as follows:
Total work input (Wtotal) = Useful work output (W) / Efficiency
Wtotal = 1593.12 Joules / 0.875
Wtotal = 1823.07 Joules
The total work input is the product of the force applied on the rope and the distance the rope is pulled. Let's assume the distance the rope is pulled is 'x' meters.
Therefore, Wtotal = Force * Distance
1823.07 Joules = 648N * x meters
Now, rearranging the equation to solve for x:
x = 1823.07 Joules / 648N
x ≈ 2.82 meters
Hence, approximately 2.82 meters of rope must be pulled to lift the 105 kg desk 2.46 meters using the given pulley system with an efficiency of 87.5%.