a boy pulls a 15 kg over level ground by a rope with a force of 50 newtons at 30 degrees above the horizontal, the coefficients of friction between the box and the ground are 0.3 and 0.4, calculate the normal force exerted on the box to the ground, calculate the acceleration of the box, the boy suddenly increases his pulling force on the rope, what happens to the normal force exerted on the box does it increase, decrease, or stay the same
and what are your thoughts?
To find the normal force exerted on the box, we need to understand the forces acting on it. In this case, the only vertical force acting on the box is the gravitational force, which is equal to the weight of the box. The weight is calculated by multiplying the mass (15 kg) by the acceleration due to gravity (9.8 m/s^2):
Weight = mass × acceleration due to gravity
= 15 kg × 9.8 m/s^2
= 147 N
Since the box is on level ground, there is no vertical acceleration, and the normal force exerted on the box by the ground is equal to the weight, which is 147 N.
To calculate the acceleration of the box, we need to break the applied force into horizontal and vertical components. The horizontal component of the force can be calculated using trigonometry:
Horizontal force = applied force × cos(angle)
= 50 N × cos(30 degrees)
≈ 43.3 N
The frictional force acts in the opposite direction of motion and is given by the equation:
Frictional force = coefficient of friction × normal force
Using the given coefficient of friction (0.3), we can calculate the frictional force:
Frictional force = 0.3 × normal force
At maximum static friction, the frictional force equals the horizontal force, so:
0.3 × normal force = 43.3 N
Normal force = 43.3 N / 0.3
Normal force ≈ 144.3 N
Therefore, the normal force exerted on the box is approximately 144.3 N.
Now, let's consider what happens when the boy suddenly increases his pulling force on the rope. If the boy increases his force and the box starts to accelerate, the frictional force will also increase. The maximum static frictional force is determined by the coefficient of friction and the normal force. As long as the applied force does not exceed the maximum static frictional force, the box will not start moving.
So, when the boy increases his pulling force, the maximum static frictional force will increase. To keep the box at rest, the normal force will also need to increase in order to maintain the balance between the applied force and the maximum static frictional force.
Therefore, when the boy increases his pulling force, the normal force exerted on the box will increase as well.