I'm stumped with this physics problem. Please help!?

Question

A student tries to raise a chain consisting of three identical links. Each link has a mass of 380 g. The three-piece chain is connected to a string and then suspended vertically, with the student holding the upper end of the string and pulling upward. Because of the student's pull, an upward force of 15.0 N is applied to the chain by the string. Use Newton's laws to answer the following questions.

a. Find the acceleration of the chain.
Take the free fall acceleration to be g = 9.80 m/s^2.


b. Find the force exerted by the top link on the middle link.


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Answer 1

The total mass of the chain is 3*380g The force applied to the whole chain is 15.0N. There is also a downward force from gravity, equal to m*g. The total force on the chain is then 15.0N-3*380*g From Newton's second law, F = m*a, or a = F/m; you have F and you have m (3*380g), so you can calculate a. The only difficulty here is keeping the units straight (newton =kg*m/sec^2, and your masses are given in grams, not kg; you should convert them.)

The lower two links are accelerating at rate a, and the accelerating force must come from the connection between the top link and middle link. That force must be equal to 2*380*a plus the gravitational force, 2*380*g. Think about it: if the chain was not accelerating, the force from the top link to the middle must be the weight of the two lower links.

Answer 2

Each link is 380 g so all three are 1.14 kg. Therefore the total -downwards- force on the string is F=ma
f= 1.14kg*9.8m/s² = 11.172 N downwards. But the student is exerting 15N upwards so the -net- force acting on the chain is 15 - 11.172 = 3.828 N -upwards-.

Now, a mass of 1.14 kg with 3.828N acting on it will accelerate at a = F/m = 3.828/1.14 = 3.358 m/s² and it will be -upwards-.

The force on the top link (exerted by the student) is 15N. The force exerted on the 2'nd link is 15N minus the force exerted by the 1'st link (caused by it's being in a gravitational acceleration field). So
F = 15 - ma = 15 - .38*9.8 = 11.276N

Hope that helps ☺


Doug

Answer 3

total weight of chain = 1140 g = 1.14kg

Force due to gravity = 1.14kg x g = 11.172 N

Net force = 15N - 11.172 = 3.828N upwards

Acceleration of chain = F/m = 3.828 / 1.14 = 3.36 m/s^2

The top link exerts a force enough to accelerate the other two links at 3.36 m/s^2, force required is then F = ma = 3.36 x .76kg = 2.55N

Answer 4

Answer to the 'a' part is 3.36 m/s^2.

The answer to the B part is 10 N.

Let the required force be F.
Then F - 0.38*2*9.8 = 0.38*2*3.36, which gives F as 10 N.

Answer 5

for a. use the formula, force = mass x acceleration