#1 Physics 1135 Homework for Recitation 6: Newton\'s 3rd law, coupled objects Tw

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Physics 1135 Homework for Recitation 6: Newton's 3rd law, coupled objects Two crates with treasure, a small one with mass m=100kg and a large one with mass M=300kg are connected by a massless rope and are on a frozen lake which you may assume to be frictionless. A rope is attached to the front of the heavy crate, and a band of dwarves, which stand at the shore and dig their heels into the soil so they do not slip, are pulling with a horizontal force that causes the crates to accelerate with an acceleration of 2 m/s2. Determine the magnitude of the pulling force and the tension in the rope that connects the crates. What would the tension in the rope connecting the crates be if the rope were attached to the front of the small crate, and the dwarves pulled with the same force as you found in part a?

Explanation / Answer

a) considering both blocks as a single system

and using newton's 2nd law,

Fnet = (mass of system) x acc. of system

P = (m + M)a

P = (100 + 300) x 2 = 800 N

now using Fnet = ma on small block.

T = 100 x 2 = 200 N

(it can be find by larger mass, P - T = Ma

800 - T = (300 x 2)

T = 800 - 600 = 200 N)

b) considering both as a single system,

so P = (m + M)a

P =( 100 + 300)2 = 800 N

for tension on larger block,

T = Ma = 300 x 2 = 600 N

or using small block,

P - T = ma

800 - T = 100 x2 = 200

T = 800- 200 = 600 N

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