A box is pulled along a level floor at a constant speed by a rope that makes a 45 degree angle with the floor. The box weighs 100N. The coefficient of sliding friction is 0.75. The normal force exerted on the box by the floor is?
M*g = 100 N.
Fn = 100*Cos0 - Fap*sin45 = Normal force
Fn = 100 - 0.707Fap
Fk=u*Fn = 0.75(100-0.707Fap)=75-0.53Fap
Fap-Fk = M*a
Fap-75 + 0.53Fap = M*0 = 0
1.53Fap = 75
Fap = 49 N. = Force applied.
Fn = 100-0.707Fap = 100 - 0.707*49 = 65.4 N. = Normal force.
To find the normal force exerted on the box by the floor, we need to consider the forces acting on the box and use Newton's second law of motion.
First, let's draw a free body diagram of the box:
1. The weight of the box acts vertically downward with a force of 100N.
- We can think of this force as the gravitational force acting on the box. It is equal to the mass of the box (m) multiplied by the acceleration due to gravity (g), which is approximately 9.8 m/s².
2. The force of friction opposes the motion of the box.
- The coefficient of sliding friction (μ) is given as 0.75. We can use this value to calculate the force of friction which is equal to μ times the normal force.
- The force of friction acts parallel to the surface and opposes the motion of the box, so it points in the opposite direction to the force applied by the rope.
3. The force applied by the rope pulls the box along the floor.
- The angle between the rope and the floor is given as 45 degrees. We need to resolve this force into its horizontal and vertical components.
Now, let's use the information we have to calculate the normal force.
Since the box is at a constant speed, that means the net force acting on it must be zero. This means that the force pulling the box forward due to the rope is equal to the force of friction acting against it in the opposite direction.
To find the force of friction, we need to calculate the horizontal component of the force applied by the rope.
The horizontal component of the force applied by the rope can be calculated using trigonometry. Since the angle between the rope and the floor is 45 degrees, the horizontal component is given by:
Force_horizontal = Force_applied * cos(angle)
Substituting the values:
Force_horizontal = Force_applied * cos(45°)
Since the force applied by the rope is not given in the question, we need to assume it is equal to the weight of the box (100N) to maintain a constant speed.
Force_horizontal = 100N * cos(45°)
Next, we can calculate the force of friction:
Force_friction = coefficient_of_friction * Normal_force
Substituting the given value of the coefficient of sliding friction (0.75):
Force_friction = 0.75 * Normal_force
Since the force pulling the box forward due to the rope is equal to the force of friction:
Force_horizontal = Force_friction
Now we can set up an equation:
100N * cos(45°) = 0.75 * Normal_force
Solving this equation will give us the value of the normal force exerted on the box by the floor.