Two movers are attempting to push a 300kg piece of furniture across the floor. One man pulls horizontally with a force of 45N while the other pulls with 80N at a 25 degree angle. If the crate slides with an acceleration of 9.15m/s^2, what is the frictional force between the floor and the furniture?

M*g = 300 * 9.8 = 2940 N. = Wt. of furniture.

Fk = Force of kinetic friction.

F1 = 45 N. F2 = 80*Cos25 = 72.5 N.

F1+F2 - Fk = M*a. Fk = ?.

To find the frictional force between the floor and the furniture, we can start by calculating the net force acting on the furniture.

1. First, let's convert the pulling force applied by the first mover to the horizontal component only. Since he is pulling horizontally, the entire 45N force can be considered the horizontal force.

2. Next, let's calculate the horizontal component of the force applied by the second mover. This can be found using the formula: F_horizontal = F * cos(angle), where F is the force applied and the angle is 25 degrees.

F_horizontal = 80N * cos(25°)
F_horizontal = 80N * 0.9063
F_horizontal = 72.5N

3. Now that we have the horizontal forces, we can calculate the net force in the horizontal direction.

Net force = F_horizontal by first mover - F_horizontal by second mover
= 45N - 72.5N
= -27.5N

Negative sign indicates that the net force is in the opposite direction of the applied force. This means there is a frictional force acting against the motion of the furniture.

4. Finally, we can use Newton's second law, F = ma, to determine the frictional force. Since the furniture is accelerating, the net force acting on it is equal to the product of its mass and acceleration.

F_net = m * a

Frictional force = m * a
= 300kg * 9.15m/s²
= 2745N

Therefore, the frictional force between the floor and the furniture is 2745N.