# Problem 540 | Friction on Wedges

**Problem 540**

As shown in Fig. P-540, two blocks each weighing 20 kN and resting on a horizontal surface, are to be pushed apart by a 30° wedge. The angle of friction is 15° for all contact surfaces. What value of P is required to start movement of the blocks? How would this answer be changed if the weight of one of the blocks were increased by 30 kN?

**Solution 540**

$\Sigma F_H = 0$

$R_1 \sin 15^\circ = R_2 \cos 30^\circ$

$R_1 = 3.346R_2$

$\Sigma F_V = 0$

$R_1 \cos 15^\circ = R_2 \sin 30^\circ + 20$

$(3.346R_2) \cos 15^\circ = R_2 \sin 30^\circ + 20$

$2.732R_2 = 20$

$R_2 = 7.32 \, \text{ kN}$

From the FBD of the upper block

$\Sigma F_V = 0$

$P = 2R_2 \sin 30^\circ$

$P = 2(7.32) \sin 30^\circ$

$P = 7.32 \, \text{ kN}$ *answer*

When one block weigh 50 kN and the other is 20 kN, the first to impend when movement starts is the 20 kN block. Thus the reaction R_{2} = 7.32 kN, similar to the above value of R_{2}. Thus, the answer which is P = 7.32 kN will not change. See the free body diagram below and note that the friction reaction f_{3} is not equal to the maximum available friction under the 50 kN block.