A testing laboratory wants to determine if a new widget can withstand large acceleration and decelerations. To find out, they glue a 5.0kg widget to a test stand that will drive it vertically up and down. At 0 seconds the widget is at an acceleration of 19.6m/s^2. It reaches 0 at 1/2 a second and drops to -19.6m/s^2 by 1 sec The widget decelerates at 39.2m/s^2 every second.

a) Identify the forces acting on the widget and draw a free body diagram.

I'm already stuck here. I know there's a normal force and a gravitational force.

b) Determine the value of ny, the y-component of the normal force acting on the widget during the first second of motion. Give your answer as a graph of ny versus t.

Why is there a y-component to the normal force? Since it's accelerating vertically wouldn't there be no x-component, therefore the y-component would be the whole normal force?

a) In order to identify the forces acting on the widget and draw a free body diagram, we need to consider the motion of the widget and the forces involved.

1. Gravitational force (fₘg): This force acts vertically downward due to the Earth's gravitational pull on the widget. Its magnitude can be calculated using the formula fₘg = m * g, where m is the mass of the widget and g is the acceleration due to gravity (approximately 9.8 m/s^2).

2. Normal force (fₙ): This force acts perpendicular (normal) to the surface of contact between the widget and the test stand. It counteracts the gravitational force and keeps the widget from sinking into the test stand. It has both x and y components, but for this question, we are focusing on the y-component.

b) The y-component of the normal force (ny) can be determined by analyzing the acceleration and deceleration of the widget during the first second of motion.

Initially, at 0 seconds, the widget experiences an acceleration of 19.6 m/s^2 upwards. This means the net force acting on the widget in the y-axis direction is the difference between the gravitational force and the applied force (f_net = fₙ - fₘg).

Using Newton's second law (f_net = m * a), we can write the equation as follows:
fₙ - fₘg = m * a

Simplifying the equation, we get:
ny - mg = ma

Considering the mass of the widget (m = 5.0 kg) and the acceleration (a = 19.6 m/s^2), we can substitute these values and solve for ny:
ny - (5.0 kg) * (9.8 m/s^2) = (5.0 kg) * (19.6 m/s^2)

Solving the equation, we find:
ny = (5.0 kg) * (19.6 m/s^2) + (5.0 kg) * (9.8 m/s^2)

To graph ny versus t during the first second of motion, we need to consider how the acceleration changes over time. The widget reaches 0 acceleration at 1/2 a second and then decelerates at a rate of 39.2 m/s^2 per second.

We can divide the first second of motion into two intervals:
1. From t = 0 to t = 1/2 second: Acceleration is constant at 19.6 m/s^2.
2. From t = 1/2 second to t = 1 second: Deceleration is constant at 39.2 m/s^2.

To plot ny versus t, calculate ny at various time points within these intervals and plot them on a graph.

Please note that without specific values for time intervals or acceleration intervals, we cannot provide an accurate graph.