Final answer:
A force of 120 N is required to stop an 80 kg skateboarder traveling at 6 m/s in 4 seconds, using the concept of impulse and Newton's second law of motion.
Step-by-step explanation:
To calculate the force needed to stop a skateboarder with a mass of 80 kg traveling at a velocity of 6 m/s in a time span of 4 seconds, one can utilize the concept of impulse and Newton's second law of motion. The impulse equals the change in momentum, and according to Newton's second law, force is the rate of change of momentum. Here's how you calculate it:
Calculation Details
First, find the skateboarder's initial momentum:
Initial momentum = mass x initial velocity
Initial momentum = 80 kg x 6 m/s
Initial momentum = 480 kg·m/s
Since he needs to stop, his final momentum will be 0 kg·m/s.
Change in momentum = final momentum - initial momentum
Change in momentum = 0 kg·m/s - 480 kg·m/s
Change in momentum = -480 kg·m/s (negative because the direction is opposite to the initial velocity)
Now, the impulse can be calculated, which is force x time:
Impulse = force x time
-480 kg·m/s = force x 4 s
force = -480 kg·m/s / 4 s
force = -120 N
The negative sign indicates the force is applied in the opposite direction of motion. Therefore, a force of 120 N is required to stop the skateboarder in 4 seconds.