Using a rope, a child pulls a box across a rough floor at a constant speed. The tension in the rope is 105 N and the rope makes an angle of 37 degrees with the horizontal. Find the friction force acting on the box (due to the rough floor).
the rope is pulling, and lifting ...
forcelifting=105sin37
force pulling=105cos37
forcepulling-frictionforce=ma=zero
the problem is too easy...friction force=pulling force.
To find the friction force acting on the box, we need to analyze the forces acting on the box and utilize Newton's laws of motion.
First, let's break down the forces acting on the box:
1. Tension Force (T): The tension force in the rope, which is acting parallel to the floor, is equal to 105 N.
2. Weight Force (W): The force due to gravity pulling the box downward, which can be calculated by multiplying the mass of the box (m) by the acceleration due to gravity (g). Since the box is on a horizontal surface, the weight force acts vertically downward.
3. Friction Force (F): The force opposing the motion of the box across the rough floor. This force acts parallel to the floor and in the opposite direction as the tension force.
In this problem, we want to find the value of the friction force (F). We can determine this by analyzing the vertical and horizontal components of the tension force.
1. The vertical component of the tension force is T * sin(37°). Since the box is moving at a constant speed, the vertical component of the tension force must balance the weight force (W).
W = T * sin(37°)
2. The horizontal component of the tension force is T * cos(37°). This component creates the friction force (F) acting on the box.
F = T * cos(37°)
Now, let's substitute the given value for the tension force:
F = 105 N * cos(37°)
Using a calculator, we can evaluate the expression:
F ≈ 84.525 N
Therefore, the friction force acting on the box (due to the rough floor) is approximately 84.525 N.