Question

what is the minimum coeffecient of static friction μmin required between the ladder and the ground so that the ladder does not slip? express μmin in terms of m1 , m2 , d , l , and θ .

Answer 1

The minimum coefficient of static friction (μmin) required between the ladder and the ground can be expressed as tan(β).

Step-by-step explanation:

The minimum coefficient of static friction (μmin) required between the ladder and the ground so that the ladder does not slip can be expressed in terms of m1, m2, d, l, and θ. In this case, we have a ladder resting against a wall with an angle of inclination (β) between the ladder and the rough floor. To find μmin, we can use the equation μmin = tan(β). The normal force (N) can be calculated using the equation N = m1g + m2g, where m1 represents the mass of the ladder and m2 represents the mass of any objects hanging on the ladder.

Answer 2

The minimum coefficient of static friction required between the ladder and the ground so that the ladder does not slip is (m1*g*cos(θ))/(m2 + m1*sin²(θ)).

Step-by-step explanation:

In order for the ladder to not slip, the force of static friction between the ladder and the ground must be equal to or greater than the force attempting to cause the ladder to slide. The force attempting to cause the ladder to slide is the horizontal component of the weight of the ladder, which is given by m1*g*sin(θ), where m1 is the mass of the ladder and θ is the inclination angle.

The force of static friction is given by μ* N, where N is the magnitude of the normal force. The normal force can be split into two components: N = N1 + N2, where N1 is the vertical component of the weight of the ladder and N₂ is the force exerted by the wall on the ladder.

Since the ladder is not slipping, N₂ can be equated to the force of static friction: N₂ = μ* N1. Substituting the expressions for N₁ and N₂, we get μ = (m1*g*cos(θ))/(m₂ + m1*sin²(θ)). Therefore, the minimum coefficient of static friction required is μmin = (m1*g*cos(θ))/(m2 + m1*sin²(θ)).