Free Fall and Tension in a cable

In summary, the problem involves a crate hanging from a cable with a monkey inside sitting on a ledge. The monkey jumps off the ledge and it takes 0.125 s for him to stop at the bottom of the crate. The tension in the cable is 147 N when the monkey is on the ledge and 49.0 N while he is falling. Using the equations for slope, area, and force, the mass of the monkey is determined to be 10 kg. Using the equation for momentum, the tension in the cable is calculated to be 441 N.
  • #1
swannyboy
15
0

Homework Statement



A crate is hanging from a cable as shown in the diagram. A monkey that is inside the crate, sits on a ledge that is 1.225m above the bottom of the crate. The monkey steps off the ledge and when he hits the bottom of the ledge, it takes .125 s to stop.

The tension in the cable is 147 N when the monkey is sitting on the ledge and 49.0N while he is falling.

Calculate the tension in the c able during the .125 s that he is stopping at the bottom of the crate.
[URL]http://img130.imageshack.us/i/52884921.jpg/[/URL]

Homework Equations



Not exactly sure- it's in a booklet for my comprehensive final exam. It seems like it's mostly applications of:
slope = rise/run
Area = 1/2base x height
and F = ma

The Attempt at a Solution



Basically what I've done is this:
Tension in the string = force of gravity

Tension = mg
147N = m(9.8N/kg)
M = 15 kg total

Tension = mg
49.0 = m(9.8N/kg)
m = 5kg

So the monkey's mass is 10 kg.

When the monkey jumps off, he Accelerates at 9.8m/s^2 for 1.225meters

d=1/2vt
2.45m/v = t

A = (v2-v1)/(t2-t1)
A =(V^2)/(2.45m)
24.01 = v^2
V = 4.9m/s

D = 1/2vt
2.45m = (4.9m/s)t
t = 0.5s

I think I'm going in the right direction, but I don't know where to go from here.
 
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  • #2
Now if I try using momentum.../
F(delta_t) = m (delta_v)
= (10kg)(4.9m/s)
Impulse = 49 kgm/s

49kgm/s = F (0.125s)
F = 392 N

Fnet = fg + fa
Fnet = 49N + 392N
Fnet = 441N

So, is that what the tension would be?
 

Related to Free Fall and Tension in a cable

1. What is free fall?

Free fall is the motion of an object under the influence of gravity only. This means that the object is not experiencing any other forces, such as air resistance, and is accelerating towards the ground at a constant rate of 9.8 m/s².

2. How is tension in a cable related to free fall?

Tension in a cable is the force exerted by the cable to maintain its shape and support any objects attached to it. In free fall, the tension in the cable is equal to the weight of the object attached to it, as the object is accelerating towards the ground.

3. How does the tension in a cable change during free fall?

The tension in a cable will increase as the object attached to it accelerates towards the ground. This is because the weight of the object increases due to the acceleration, and the cable needs to exert a greater force to support it.

4. Can the tension in a cable ever be greater than the weight of the object attached to it?

Yes, the tension in a cable can be greater than the weight of the object attached to it if the object is decelerating or changing direction. In this case, the cable needs to exert a greater force to slow down or change the object's direction.

5. How does the length of the cable affect free fall and tension?

The length of the cable will affect both the free fall and tension. A longer cable will result in a longer free fall time, as the object has a greater distance to travel. It will also experience a greater tension due to the longer distance the cable needs to support the object.

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