You have setup an experiment with two 50g masses attached to strings that are connected on opposite sides of a scale that measures weight in Newtons.
a.) What is the reading on the scale?
b.) The whole system is now moving to the left at a speed of 10m/s. What is the reading on the scale?
c.) The whole system is now moving to the right at a speed of 50m/s. What is the reading on the scale.
To answer these questions, we need to consider the forces acting on the masses and the scale.
a) When the system is at rest, the only force acting on the masses is their own weight. The weight of each mass can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that the mass of each object is 50g (0.05kg), and the acceleration due to gravity is approximately 9.8m/s^2, we can calculate the weight of each individual mass.
Weight = 0.05kg * 9.8m/s^2 = 0.49N (rounded to two decimal places)
Since the masses are attached on opposite sides of the scale, the forces acting on the scale cancel each other out. Therefore, the reading on the scale will be zero.
b) When the system is moving to the left at a speed of 10m/s, there is an additional force acting on the masses due to their inertia. This force is opposing the direction of motion and is called the pseudo force.
The magnitude of the pseudo force can be calculated using the formula:
Pseudo force = mass * acceleration
Given that the mass of each object is 0.05kg and the acceleration is 10m/s^2 (opposite to the direction of motion), we can calculate the pseudo force.
Pseudo force = 0.05kg * 10m/s^2 = 0.5N (rounded to one decimal place)
Since the system is accelerating to the left, the pseudo force will be added to the weight of each mass. Therefore, the force exerted on each side of the scale will be:
Total force = Weight + Pseudo force = 0.49N + 0.5N = 0.99N (rounded to two decimal places)
Since the forces on each side of the scale are not equal, there will be a net force causing a reading on the scale. Thus, the reading on the scale will be 0.99N.
c) When the system is moving to the right at a speed of 50m/s, the same pseudo force will be acting on the masses, but in the opposite direction to the one in part b. Therefore, the pseudo force will be subtracted from the weight of each mass.
Pseudo force = 0.05kg * 50m/s^2 = 2.5N
Total force = Weight - Pseudo force = 0.49N - 2.5N = -2.01N (rounded to two decimal places)
Since the net force acts in the opposite direction to the weight, the reading on the scale will be negative (-2.01N).