Question

A block of mass 12 kg starts from rest and slides a distance of 7 m down an inclined plane making an angle of 40 degrees with the horizontal. The coefficient of sliding friction between the block and the plane is 0.4. The acceleration of gravity is 9.8 m/s². What is the net force on the block along the incline?

Answer 1

The net force on the block along the incline is approximately 29.634 N.

Step-by-step explanation:

The net force on the block along the incline can be calculated using the equation:

F_net = m * a

Where F_net is the net force, m is the mass of the block, and a is the acceleration. First, we need to calculate the acceleration of the block.

The force of gravity acting on the block can be divided into two components: a force perpendicular to the incline and a force parallel to the incline. The force perpendicular to the incline can be calculated using the equation:

F_perpendicular = m * g * cos(theta)

Where m is the mass of the block, g is the acceleration due to gravity, and theta is the angle of the incline. The force parallel to the incline can be calculated using the equation:

F_parallel = m * g * sin(theta)

The net force on the block along the incline can be calculated by subtracting the force of friction from the force parallel to the incline:

F_net = F_parallel - F_friction

The force of friction can be calculated using the equation:

F_friction = mu * F_perpendicular

Where mu is the coefficient of sliding friction. Substituting the values:

F_friction = 0.4 * (12 * 9.8 * cos(40))

F_friction = 46.536 N

Now we can calculate the force parallel to the incline:

F_parallel = 12 * 9.8 * sin(40)

F_parallel = 76.170 N

Substituting the values into the net force equation:

F_net = 76.170 - 46.536

F_net = 29.634 N

Therefore, the net force on the block along the incline is 29.634 N.