Question w/ work and friction

[badboyben03]

Sally applies a horizontal force of 520 N with a rope to drag wooden crate across a floor with a constant speed. The rope tied to the crate is pulled at an angle of 84.5°

How much force is exerted by the rope on the crate and what work is done by the floor through force of friction between the floor and the crate?

how can i find the force on rope and force of friction w/o knowing the distance?

 

[HallsofIvy]

Draw the force diagram. The force along the rope, horizontally, and vertically form a right triangle with angle 84.5°.

Since you are told that the horizontal force is 520 N, and "horizontal over hypotenuse" is cosine, we have 520/F= cos(84.5°) or F= 520/cos(84.5) where F is the force in the direction of the rope (hypotenuse). That is the force the rope applies to the crate and therefore, the force the crate applies to the rope (in the opposite direction).

If there were a net horizontal force on the crate, the crate would accelerate. Since it is moving at constant speed, the friction force must be exactly the same as the horizontal force, 520 N, but in the opposite direction.

 

[M98Ranger]

To find the force exerted by the rope on the crate, we can use trigonometry to break down the applied force of 520 N into its horizontal and vertical components. The horizontal component would be equal to 520 Ncos84.5°, which is approximately 78 N. This is the force exerted by the rope on the crate.

To calculate the work done by the floor through the force of friction, we can use the formula W = Fd, where W is work, F is force, and d is distance. Since the crate is moving at a constant speed, we know that the net force acting on it is zero. This means that the force of friction must be equal in magnitude to the force applied by the rope, which we calculated to be 78 N. However, since we do not know the distance, we cannot calculate the work done by the floor. We would need to know the distance to determine the displacement of the crate and thus calculate the work done by the floor.

In order to find the force of friction, we would also need to know the coefficient of friction between the crate and the floor. This coefficient represents the amount of friction present between the two surfaces and can be different for different materials. Without this information, it is not possible to accurately calculate the force of friction.

In summary, without knowing the distance and the coefficient of friction, we cannot accurately determine the force of friction or the work done by the floor. It is important to have all the necessary information in order to accurately solve physics problems.