Answer:
The normal force exerted on a book resting on a surface inclined at 32 degrees above the horizontal can be calculated using the equation:
Normal force = Weight * cos(angle)
Weight is the force exerted by gravity on the book and can be calculated using the equation:
Weight = mass * gravity
In this case, the mass of the book is given as 2.7 kg. The value of gravity is approximately 9.8 m/s^2.
So, Weight = 2.7 kg * 9.8 m/s^2 = 26.46 N.
Now, substituting the values into the equation for normal force:
Normal force = 26.46 N * cos(32 degrees) = 22.39 N.
Therefore, the normal force exerted on the book is approximately 22.39 N.
When the angle of the inclined surface is reduced, the normal force will decrease. This is because the normal force is perpendicular to the surface and acts to support the weight of the book. As the angle of the surface decreases, the component of the weight acting perpendicular to the surface also decreases, resulting in a decrease in the normal force.
To understand this concept, imagine a book placed on a flat surface. The weight of the book acts vertically downwards, and the normal force acts vertically upwards to balance the weight. Now, if you tilt the surface, the weight of the book can be split into two components - one parallel to the surface and one perpendicular to the surface. The component parallel to the surface causes the book to slide down, and the component perpendicular to the surface is balanced by the normal force.
As the angle of the surface decreases, the component of the weight perpendicular to the surface becomes smaller, requiring a smaller normal force to balance it. Hence, the normal force will decrease when the angle of the inclined surface is reduced.
Step-by-step explanation: