Question

The block moves up an incline with constant speed. What is the total work Wtotal done on the block by all forces as the block moves a distance L = 4.00 m up the incline? Include only the work done after the block has started moving at constant speed, not the work needed to start the block moving from rest.

Answer 1

The total work done on the block as it moves up the incline with constant speed is equal to the work done by gravity. The work done by gravity is given by the formula W = mg, where m is the mass of the block, g is the acceleration due to gravity, and h is the vertical height the block moves.

Step-by-step explanation:

To find the total work done on the block as it moves up the incline with constant speed, we need to consider the work done by gravity and the work done by the normal force.

The work done by gravity is given by the formula W = mg, where m is the mass of the block, g is the acceleration due to gravity, and h is the vertical height the block moves. In this case, the block moves a distance L = 4.00 m up the incline, so the vertical height is h = L*sin(theta), where theta is the angle of the incline.

The work done by the normal force is zero because the normal force is perpendicular to the displacement of the block. Therefore, the total work done on the block is equal to the work done by gravity:

Wtotal = mg = mgL*sin(theta)

Answer 2

zero

Step-by-step explanation:

Since the work on the block is the sum of the works done by every force acting on the block:

Wtotal = Wk + Wn + Wg

Wk ; work done by the friction force, Fk

Wn: work done by the normal force, Fn

Wg: work done by the gravity force, Fg

Since, by definition of work:

Wk = Fk*L*cos(180°) = - Fk*L

Wn = Fn*L*cos(90°) ) = 0

Wg = Fg*L*cos(90-∅) = Fg*L*sin(∅)

Wtotal = - Fk*L + 0 + Fg*L*sin(∅) ----- (1)

Since the block moves to constant velocity, by 2° Newton's law: the sum of all forces are zero.

Using diagram of all forces, is posible demostrate:

Fk = Fg*sin(∅)

Reeplacing in the (1) expression:

Wtotal = 0