Calculate the work done by the effort and the effort applied when a system of 6polley is used to raise a load of 600N through a distance of 30m. The work done against friction is 2000J.
total effort work ... [6 * 30 m * (600 / 6) N] + 2000J = 20000 J
effort distance ... 6 * 30 m = 180 m
effort applied = 20000 J / 180 m = ? N
To calculate the work done, we need to understand the concept of work and how it is calculated.
Work is defined as the force applied to an object multiplied by the distance over which the force is applied. Mathematically, work (W) is given by the equation:
W = F * d * cos(theta)
Where:
W: Work done (in joules, J)
F: Applied force (in newtons, N)
d: Distance over which the force is applied (in meters, m)
theta: Angle between the force and the direction of displacement (if applicable, not used in this problem)
In this question, we are given the force against friction (2000J) and the load to be raised (600N). However, we need to find the effort applied.
Since the system consists of 6 pulleys, it implies that the load is distributed among them, resulting in the effort being less than the load. In such systems, the work done by the effort is equal to the work done against the load plus the work done against friction.
Therefore, the equation can be written as:
Work done by effort = Work done against load + Work done against friction
Now let's calculate the work done against the load:
Work done against load = Load * Distance lifted
Given:
Load = 600N
Distance lifted = 30m
Work done against load = 600N * 30m = 18,000J
Now, we can calculate the work done by the effort:
Work done by effort = Work done against load + Work done against friction
Work done by effort = 18,000J + 2000J = 20,000J
Thus, the work done by the effort is 20,000J.
20180
Why did the pulleys go to the circus? Because they wanted to lift some serious weight! Alright, let's get down to business and calculate that work done.
To start, we need to find the work done by the effort (W_effort) and the total work done (W_total). We can use the formulas:
W_effort = W_total - Work against friction
Given that the work done against friction is 2000J, we can substitute it into the equation:
W_effort = W_total - 2000J
Now let's calculate the total work done (W_total):
W_total = force * distance
W_total = 600N * 30m
W_total = 18000J
Now we can substitute the value of W_total into the first equation:
W_effort = 18000J - 2000J
W_effort = 16000J
So, the work done by the effort is 16000J. Keep in mind that the work done against friction doesn't contribute to the effort applied. It's just the system having some fun with friction along the way!
To calculate the work done by the effort (W_effort) and the work done by the effort applied (W_applied), we can use the formula:
Work = Force x Distance
Given:
Load (Force) = 600N
Distance = 30m
Work against friction = 2000J
First, let's calculate the work done against friction (W_friction):
W_friction = 2000J
Next, we'll calculate the total work done (W_total):
W_total = Force x Distance
W_total = 600N x 30m
W_total = 18000J
Since the total work consists of the work done by the effort and the work done against friction, we have the equation:
W_total = W_effort + W_friction
Therefore, we can rearrange the equation to find the work done by the effort:
W_effort = W_total - W_friction
W_effort = 18000J - 2000J
W_effort = 16000J
Now, let's calculate the work done by the effort applied:
W_applied = W_total - W_effort
W_applied = 18000J - 16000J
W_applied = 2000J
So, the work done by the effort is 16000J, and the work done by the effort applied is 2000J.