Respuesta :
Answer:
The speed after being pulled is 2.4123m/s
Explanation:
The work realize by the tension and the friction is equal to the change in the kinetic energy, so:
[tex]W_T+W_F=K_f-K_i[/tex] (1)
Where:
[tex]W_T=T*x*cos(0)=32N*3.2m*cos(30)=88.6810J\\W_F=F_r*x*cos(180)=-0.190*mg*x =-0.190*10kg*9.8m/s^{2}*3.2m=59.584J\\ K_i=0\\K_f=\frac{1}{2}*m*v_f^{2}=5v_f^{2}[/tex]
Because the work made by any force is equal to the multiplication of the force, the displacement and the cosine of the angle between them.
Additionally, the kinetic energy is equal to [tex]\frac{1}{2}mv^{2}[/tex], so if the initial velocity [tex]v_i[/tex] is equal to zero, the initial kinetic energy [tex]K_i[/tex] is equal to zero.
Then, replacing the values on the equation and solving for [tex]v_f[/tex], we get:
[tex]W_T+W_F=K_f-K_i\\88.6810-59.5840=5v_f^{2}\\29.097=5v_f^{2}[/tex]
[tex]\frac{29.097}{5}=v_f^{2}\\\sqrt{5.8194}=v_f\\2.4123=v_f[/tex]
So, the speed after being pulled 3.2m is 2.4123 m/s
