A child has a mass of 36kg and is sitting on a seat on an amusement park ride. The ride makes the seat move up and down. Determine the normal force acting on the child when the child is:
a) Moving up at a constant velocity of 12m/s.
b) Moving down at a constant velocity of 14m/s.
c) Accelerating down at 1.8m/s^2.
To determine the normal force acting on the child in each scenario, we need to consider the forces acting on the child and apply Newton's second law.
a) When the child is moving up at a constant velocity of 12 m/s, the normal force is equal in magnitude and opposite in direction to the gravitational force acting on the child.
The gravitational force (or weight) can be calculated using the formula:
Weight = mass × acceleration due to gravity
Weight = 36 kg × 9.8 m/s²
Weight = 352.8 N
Since the child is moving up at a constant velocity, there is no net force acting on the child. Therefore, the normal force is equal in magnitude to the weight, which is 352.8 N.
b) When the child is moving down at a constant velocity of 14 m/s, the normal force is again equal in magnitude and opposite in direction to the gravitational force.
Using the same formula as before, the weight of the child is:
Weight = 36 kg × 9.8 m/s² = 352.8 N
Since the child is moving down at a constant velocity, there is no net force acting on the child. Therefore, the normal force is equal in magnitude to the weight, which is 352.8 N.
c) When the child is accelerating down at 1.8 m/s², we need to consider the net force acting on the child.
The gravitational force acting on the child is:
Weight = 36 kg × 9.8 m/s² = 352.8 N
The net force can be calculated using Newton's second law:
Net force = mass × acceleration
Net force = 36 kg × (-1.8 m/s²) (Note: the acceleration is negative because it is in the opposite direction of the gravitational force)
Net force = -64.8 N
The negative sign indicates that the net force is acting in the opposite direction of the gravitational force.
To determine the normal force, we can find the difference between the gravitational force and the net force:
Normal force = Weight - Net force
Normal force = 352.8 N - (-64.8 N)
Normal force = 417.6 N
Therefore, when the child is accelerating down at 1.8 m/s², the normal force acting on the child is 417.6 N.