Two objects with masses 4.90 and 2.10 hang 0.800 above the floor from the ends of a cord 7.20 long passing over a frictionless pulley. Both objects start from rest.

Question

Two objects with masses 4.90 and 2.10 hang 0.800 above the floor from the ends of a cord 7.20 long passing over a frictionless pulley. Both objects start from rest.

Find the maximum height reached by the 2.10 object.

The heavier object will move .8 m down, the lighter will move up an additional .8m.

max height= initial height+movement up.

but how do u find the initial height?

Thanks

Answer 1

Hey Ben,

alright first you have to determine the acceleration of the system.
Let m1=2.1kg and m2=4.9kg
Use
F=ma
m2g-m1g=m2a+m1a
(m2-m1)g=(m2+m1)a
a= (m2-m1)(g)/(m2+m1)
= (4.9-2.1)(9.8)/ (4.9+2.1)
=3.92 ms^-2
Now we must determine the speed of m1
we use
v^2=u^2+2as
we know that m1 was at rest so u=0 m/s
and also we know that m2 will go all the way down so m1 moves up 0.8m so s=0.8 m
v^2=0+(2)(3.92)(0.8)
v^2= 6.272
v=2.5044 m/s

Now we know that m1 is (0.8+0.8)m above the ground as m2 goes down to the floor

So we add 1.6m to the max height

To calculate max height
use formula
h=V^2/2g
= (2.5044)^2/ (2 x 9.8)
=0.32m
so add 1.6m to max height
0.32+1.60=1.92m

HOPE THIS HELPS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 2

"so add 1.6m to max height

0.32+1.60=1.92m"

Sorry I meant max height is = 0.32+1.60=1.92m

Answer 3

To find the initial height of the lighter object, you need to consider the distance both objects move in the system.

In this scenario, the 4.90 kg object moves downward by 0.800 m. Since the pulley is frictionless, the lighter 2.10 kg object will move upward by the same distance, which is also 0.800 m.

To determine the initial height of the lighter object, we can calculate it by subtracting the total distance moved by the lighter object from the total length of the cord. Here's the calculation:

Total distance moved by the lighter object = 0.800 m
Total length of the cord = 7.20 m

Initial height of the lighter object = Total length of the cord - Total distance moved by the lighter object

Initial height = 7.20 m - 0.800 m = 6.40 m

So, the initial height of the lighter object is 6.40 meters. With this information, you can now calculate the maximum height reached by the 2.10 kg object by adding the initial height and the distance moved upwards.