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Could anybody of you verify my answers here please... it's really important for me to know if I'm doing it right!

A mass m2= 10 kg slides on a frictionless table. The coefficients of static and kinetic friction between m2 and m1 = 5 kg are us= 0.6 and uk= 0.4.

http://img508.imageshack.us/img508/6309/tableproblem3tq.th.gif [Broken]

a) What is the maximum acceleration of m1?

b) What is the maximum value of m3 if m1 moves with m2 without slipping?

c) If m3= 30 kg, find the acceleration of each body and the tension in the string.

A mass m2= 10 kg slides on a frictionless table. The coefficients of static and kinetic friction between m2 and m1 = 5 kg are us= 0.6 and uk= 0.4.

http://img508.imageshack.us/img508/6309/tableproblem3tq.th.gif [Broken]

a) What is the maximum acceleration of m1?

*fsmax= us * Fn= us*m*g= 0.6 * 5 *9.81= 79.43 N*

F= m*a so F on m1= m1 * atot. Because F on m1 needs to equal fsmax 79,43= 5 * a and therefore a= 79,43/5= 15,886 m/sF= m*a so F on m1= m1 * atot. Because F on m1 needs to equal fsmax 79,43= 5 * a and therefore a= 79,43/5= 15,886 m/s

^{2}b) What is the maximum value of m3 if m1 moves with m2 without slipping?

*The dragging force is T= Fz3= m3 g.*

T= mtot * atot= 15 * 15.886= 238.29 N

m3= 238.29/9.81=24.29 kgT= mtot * atot= 15 * 15.886= 238.29 N

m3= 238.29/9.81=24.29 kg

c) If m3= 30 kg, find the acceleration of each body and the tension in the string.

*For m1:*

Fres= fk= uk * Fn = 0.4 * m1 * 9.81= 19.62 N

Fres= m1 * a therefore a= 19.62/5= 3.924 m/s

For m2:

Fres= T- fk = Fzm3 - fk= m3 * g - uk * m1 * g= 30* 9.81 - 0.4 * 5 * 9.81= 274.68 N

Fres= m2 * a therefore a= 274.68/ 10= 27.47 m/s

For m3:

Fres= Fz= m3 * g= 30 * 9.81= 294.3 N

Fres= m3 * a therefore a= 294.3/30= 9.81 m/s

Fres= fk= uk * Fn = 0.4 * m1 * 9.81= 19.62 N

Fres= m1 * a therefore a= 19.62/5= 3.924 m/s

^{2}For m2:

Fres= T- fk = Fzm3 - fk= m3 * g - uk * m1 * g= 30* 9.81 - 0.4 * 5 * 9.81= 274.68 N

Fres= m2 * a therefore a= 274.68/ 10= 27.47 m/s

^{2}For m3:

Fres= Fz= m3 * g= 30 * 9.81= 294.3 N

Fres= m3 * a therefore a= 294.3/30= 9.81 m/s

^{2}
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