Paul’s 10 kg baby sister Susan sits on a mat. Paul pulls the mat across the floor using a rope that is angled 30° above the floor. The tension is a constant 30 N and the coefficient of kinetic friction is 0.20. Use work and energy to find Susan’s speed after being pulled 3.0 m.

Respuesta :

Answer:

The speed of Susan is 2.37 m/s

Explanation:

To visualize better this problem, we need to draw a free body diagram.

the work is defined as:

[tex]W=F*d*cos(\theta)[/tex]

here we have the work done by Paul and the friction force, so:

[tex]W_p=F_p*d*cos(0)\\F_p=30N*cos(30^o)=26N\\W_p=26*3*(1)=78J[/tex]

[tex]W_f=F_f*d*cos(180)\\F_f=\µ*(10*9.8-30N*sin(30^o))=16.6N\\W_p=16.6*3*(-1)=50J[/tex]

Now the change of energy is:

[tex]W_p-W_f=\frac{1}{2}m*v^2\\v=\sqrt{\frac{2(78J-50J)}{10kg}}\\v=2.37m/s[/tex]

Ver imagen krlosdark12

Answer: speed= 1.95866m/s ~= 2.0 m/s

Explanation: check attachment for explanation

Ver imagen sammyayol2013
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