A 5kg object starts at rest and has a force applied to it of 10 Newtons for 2 seconds, followed by 20 Newtons for 2 seconds, followed by 30 newtons for 2 seconds, all in the same direction.
a. Determine its final velocity
b. Sketch a graph of force vs time
c. Create a different force scenario that will result in the same final velocity and sketch a force vs time graph for it.
d. What do the graphs have in common?
the final momentum is equal to the input impulses..
Input: 10*2+20*2+30*2
output: 1/2 m v^2
a. To determine the final velocity of the object, we can use the equation of motion, which states that the final velocity (Vf) is equal to the initial velocity (Vi) plus the product of acceleration (a) and time (t).
Since the object starts at rest, the initial velocity is 0 m/s. We can calculate the acceleration by dividing the total force applied to the object by its mass:
Acceleration (a) = Total Force / Mass
= (10 N + 20 N + 30 N) / 5 kg
= 12 m/s^2
Now, we can calculate the final velocity using the equation:
Vf = Vi + a*t
= 0 + 12 m/s^2 * 6 s
= 72 m/s
Therefore, the final velocity of the object is 72 m/s.
b. To sketch a graph of force vs time, we will plot the force values on the y-axis and the corresponding time values on the x-axis.
In this scenario, the force is constant at 10 N for the first 2 seconds, 20 N for the next 2 seconds, and 30 N for the following 2 seconds. The graph will show a straight horizontal line at 10 N for the first 2 seconds, followed by a straight horizontal line at 20 N for the next 2 seconds, and finally a straight horizontal line at 30 N for the last 2 seconds.
c. To create a different force scenario that will result in the same final velocity, we need to keep the total applied force and the duration the same. Let's say we apply a varying force such that for the first 4 seconds, the force is 15 N, and for the next 2 seconds, the force is 45 N.
Force vs time graph for the new scenario:
| 45 N
| ________
30 N | |
| _____|
15 N |___|
In this scenario, the force is constant at 15 N for the first 4 seconds, followed by a jump to 45 N for the next 2 seconds. The total force exerted over the 6 seconds is the same as in the original scenario, but the distribution is different.
d. Both force vs time graphs have in common that they show the applied force over time. While the values and distribution of force may vary, both scenarios result in the same final velocity of 72 m/s, indicating that the same amount of work is done on the object. Additionally, both graphs show a stepwise increase in force, followed by a period of constant force before transitioning to a different force level.