A block of mass 2 kg is placed on a flat surface inclined at an angle of 30 degrees with respect to the horizontal. A string is attached to the block and is parallel to the inclined surface. The other end of the string is attached to a pulley of negligible mass, which is fastened to the ceiling. The block is initially at rest.
a) Determine the normal force exerted on the block by the surface. b) Calculate the tension in the string.
Assume all surfaces are frictionless and g = 9.8 m/s^2.
### Solution
a) To determine the normal force exerted on the block, we need to analyze the forces acting on it. The weight of the block is given by the equation:
Weight = mass * acceleration due to gravity
= 2 kg * 9.8 m/s^2
= 19.6 N
Since the block is on an inclined surface, the normal force is not equal to the weight, but can be determined using trigonometry.
Normal Force = Weight * cosine(angle of inclination)
= 19.6 N * cos(30°)
= 16.96 N (rounded to two decimal places)
Therefore, the normal force exerted on the block by the surface is 16.96 N.
b) Now, let's determine the tension in the string. We can consider the motion of the block along the inclined surface.
First, we need to resolve the weight of the block into components parallel and perpendicular to the inclined surface. The weight component perpendicular to the inclined surface is given by:
Weight Perpendicular = Weight * sine(angle of inclination)
= 19.6 N * sin(30°)
= 9.80 N (rounded to two decimal places)
Since the block is at rest and the surface is frictionless, the net force acting on the block in the direction perpendicular to the inclined surface must be zero. Therefore, the tension in the string is equal in magnitude to the weight component perpendicular to the inclined surface.
Tension = Weight Perpendicular
= 9.80 N
Therefore, the tension in the string is 9.80 N.