In building a house of cards,two cards are propped up against each other to form an inverted V.The length of each card is 88 mm and the mass of each card is 1.8 g.Both cards are tipped at an angle of 25 $\circ$ from vertical.Calculate the magnitude and direction of the friction force acting on the base of the card on the left required to keep the card structure from collapsing. A)1.77 * 10^-2 N to right B)8.83 * 10^-2 N to right C)4.12 * 10^-3 N to right D)1.77 * 10^-2 N to left E)4.12 * 10^-3 N to left

Question

Quizplus · Accepted Answer

First, we need to find the weight of both cards:
w = mg = 1.8 g x 9.81 m/s² = 0.0176 N

Then, we can find the horizontal and vertical components of the weight force:
Fh = w x sin(25°) = 0.0075 N
Fv = w x cos(25°) = 0.0159 N

Since the structure is in equilibrium, the net force in the horizontal direction must be zero. Therefore, the friction force must be equal in magnitude and opposite in direction to the horizontal component of the weight force:
Ff = -Fh = -0.0075 N

The negative sign indicates that the friction force acts to the left, which is opposite to the direction assumed for Fh. This means the correct answer is C.

In Building a House of Cards,two Cards Are Propped Up ∘\circ∘

In Building a House of Cards,two Cards Are Propped Up $\circ$