Question

The critical angle is the largest angle for which the gravitational force does not yet cause the block to move. Finding the angle is a problem in which we deal with the block as a particle in equilibrium. Analyze Because the block is an inclined surface, the normal force perpendicular to the surface does not balance the downward force of gravity. The normal force and the force of gravity produce a net force that tends to slide the block down the incline. Static friction acts along the direction of the surface to balance this combined force of gravity and the normal force. But as the angle of Inclination Increases, the combined force tending to slide the block increases, requiring a stronger force of static friction, until the force of static friction reaches its largest possible value given by At drat point, any further increase in the angle of inclination results in unbalanced forces that accelerate the block. We need to find the largest possible angle of inclination theta for which the forces can still balance. We choose the x direction to be parallel to the inclined surface and the y perpendicular to it. Because me block Is In equilibrium, the force components must balance separately along the x direction and along the y direction. The force of gravity in the x direction (mg) sin(theta) must be balanced by the force of static friction Equation (1) sigma F_x = w epsilon sin(theta) - f_z = 0 Similarly, along the y direction, the normal force a from the surface must balance the corresponds component of force from gravity: Equation (2) sigma F_y = mu - wg cos(theta) = 0 Solving Equation (2) for wg = n(cos (theta)) - 1 and substituting into equation (1) gives Equation (3) integral_x = mgsin(theta) = (n/cos(theta)) sin(theta) - pi tan(theta) When the block is on the verge of slipping, theta = theta_t and the force of state friction has reached its maximum value f_a, max - mu n and theta_s into Equation (3) gives Equation (4) mu_s = tan (theta_c) For the measured critical angle of mu_s = 20 degree, we find from Equation (4) that Finalize Once the block starts to move at theta > theta_s, it accelerates down the incline and the force of friction is If theta is reduced to a value loss man theta_z, however, it may be possible to find an angle theta such that the block moves down the Incline with constant speed as a particle in equilibrium again (with acceleration alpha = 0). In this case, Equations (1) and (2) with f_4 replaced by f_k lead to an expression that gives the value of the coefficient of kinetic fiction where theta_c. It is possible to find an angle theta_r such that the block moves down the incline with constant speed as a particle in equilibrium again In this case, use Equations (1) and (2) with integral_x replaced by integral_k to find mu_k= tan theta_, where theta_4 < theta_4

Answer 1

Co efficient of friction is

$\mu=tan \theta=tan 25\degree=0.47$