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The person in the drawing is standing on crutches. Assume that the force exerted on each crutch by the ground is directed along the crutch, as the force vectors in the drawing indicate. If the coefficient of static friction between a crutch and the ground is 0.90 , determine the largest angle $\theta^{\mathrm{MAX}}$ the crutch can have just before it begins to slip on the floor.

$42^{\circ}$

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in this question have to deter mine orders. The maximum angle Tito that the Kerch can make with the ground in order not to sleep. We begin this question analyzing the forest at the ground exerts on the crutch off the right. So on these one, the force that the ground exerts on that crutch has two components one vertical component. We shall call f component why? And one horizontal component which I will call F component X. We can recognize this tree components as the two components off the contract forced. The vertical component is the normal force on the horizontal component is the frictional force. Now, remember that the maximum value off the frictional force is given by the static frictional coefficient times, times, the normal force and then the normal force is the Y component off the force F. Therefore, this is mu component s pines F component. Why? And these is the maximum frictional force? No, How can relate af component? Why, with the force f the complete force, we can do it as follows. This is a rectangle triangle. And here we have f component X f components. Why Tita and the Complete Force as the hype internews. Then we can use the co sign off Teeter to calculate as component white. The co sign off detail is It goes to AFC component. Why divided by F, which is the address and site off the triangle divided by the Fonte News, then af component Why is given by f climbs The crew Sign off. Teeter the reform. The maximum frictional force is given by mute static times f times a co sign off Dita. But no Newt that this then frictional force is our so equals to the X component off the force f Then if component X is ecause from US times F times lick of sign off detail, then we can also calculate f component X using the angle teeter. We can use the sign for that through the sign off. Kita Easy goes to the opposite side of the triangle. F Component X, divided by f then as components X is equals. Two f climbs this sign off tinta, then f times. The sign off Dita is ecosystem. You asked times f times their co sign off deeper. Then I can cancel out f on both sides of the equation and self form, you asked. We get the following sign off detail divided by the curse. Sign off detail, which is the tangent off Peter. Therefore, teeter marks. The maximum angle is given by the English tangent off US, which is the inverse tangent off 0.9, which is approximately 42 degrees.

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