A large engine with mass of 400 kg must be lifted 3 meters out of a truck for repair. A normal mechanic can lift with about 250 N of pulling force. They use a system of pulleys to do this. If we assume the engine starts on the ground, how long must the ropes be on the pulley to allow the mechanic to lift this engine that distance?

Question

A large engine with mass of 400 kg must be lifted 3 meters out of a truck for repair. A normal mechanic can lift with about 250 N of pulling force. They use a system of pulleys to do this. If we assume the engine starts on the ground, how long must the ropes be on the pulley to allow the mechanic to lift this engine that distance?

(hmmm... I am really not sure how to go about this problem... Can anyone help give me some ideas? Thanks!)

Answer 1

400*9.81 = 3924 Newton weight

I guess the mechanic is also on the ground?mechanical advantage needed = 3924/250 = 15.7
since pulleys do not come in fractions we will need 16 times
16*3 = 48 meters

Answer 2

You will need a MA of 2, so the rope must be twice as long as the hehttps://www.easycalculation.com/engineering/mechanical/simple-machines/mechanical-advantage-pulley.phpight raised.

Answer 3

Thanks everyone! I think those answers make sense. I ended up doing something a little different though.

First I found the velocity using 1/2mv^2i+mghi=1/2mv^2f+mghf
and got v=7.7m/s

Then I plugged that into W=change in KE
or 1/2mv^2f-1/2mv^2i = Fd
and got d=47.432m

close to Damon's answer! :D

Answer 4

Well, yes but it was the change in POTENTIAL energy m g h. The velocity is assumed negligible.

Answer 5

Oh but does the way that I did it count too? I think I might still be quite confused.

Answer 6

Sure! To solve this problem, we can use the concept of work and mechanical advantage in pulley systems.

First, let's find the work done in lifting the engine. The work (W) is given by the formula:

W = Force × Distance

In this case, the force applied by the mechanic is 250 N and the distance the engine needs to be lifted is 3 meters. Therefore, the work done in lifting the engine is:

W = 250 N × 3 m = 750 J (Joules)

Next, let's determine the mechanical advantage of the pulley system. The mechanical advantage (MA) is the ratio of the output force (the force applied to the engine) to the input force (the force applied by the mechanic). In this case, the input force is 250 N, and we need to find the output force.

Let's assume the pulley system has n pulleys. In an ideal pulley system without any friction or energy loss, the mechanical advantage can be calculated using the formula:

MA = 2n

Since we don't know the number of pulleys, let's represent it as n.

Now, let's find the output force (F_output) using the formula:

F_output = MA × F_input

Substituting the known values:

F_output = (2n) × 250 N = 500n N

Now, we can find the equation for work done using the mechanical advantage:

W = F_output × Distance

Substituting the known values:

750 J = 500n N × Distance

Let's rearrange the equation to solve for Distance:

Distance = 750 J / (500n N)

Now, we need to solve for the value of n. Since the mechanical advantage is related to the number of pulleys, we can solve for n by rearranging the formula for MA:

2n = MA
n = MA / 2

In this case, MA is the mechanical advantage we want to achieve. Since we don't know the specific value of MA, let's represent it as MA.

Now, we have the distance (in meters) and the mechanical advantage in terms of n and MA. By substituting these values into the equation, you'll be able to determine the length of the ropes on the pulley system.