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3 years ago

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A force F acts in the forward direction on a cart of mass m. A friction force ff opposes this motion. Part A Use Newton's second

law and express the acceleration of the cart. Express your answer in terms of the variables F, f, and m.

1 answer:

stellarik [79]3 years ago

5 0

Answer:

a = F-ff/m

Explanation:

According to Newton's second law of motion which states that "the rate of change in momentum of a body is directly proportional to the applied force F and acts in the direction of the force.

Mathematically;

F = ma

Since two forces acts on the cart i.e the moving force F and the frictional force Ff , we will take the sum of the forces.

∑F = ma where

m is the mass of the cart

a is its acceleration

∑F = F+(-ff )(since frictional force is an opposing force)

F - ff = ma

Dividing both sides by mass m

a = F-ff/m

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$\vec{p}_i = \vec{p}_f$

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Knowing the magnitude and directions relative to the x axis, we can find Cartesian representation of the vectors using the formula

$\ \vec{A} = | \vec{A} | \ ( \ cos(\theta) \ , \ sin (\theta) \ )$

So, our velocity vectors will be:

$\vec{v}_{1_f} = v_1 \ ( \ cos(30 \°) \ , \ sin (30 \°) \ )$

$\vec{v}_{2_f} = v_2 \ ( \ cos(-60 \°) \ , \ sin (-60 \°) \ )$

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$4.2 \ \frac{kg \ m}{s} = 0.7 \ kg \ v_1 \ cos(30 \°) + 0.7 \ kg \ v_2 \ cos(-60 \°)$

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$0 = 0.7 \ kg \ v_1 \ sin(30 \°) + 0.7 \ kg \ v_2 \ sin(-60 \°)$ .

From the last one, we get:

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