A penguin has a mass of 13 kg. The penguin slides over the ice for a distance of 50.7 m in 1.7 s before coming to a complete stop. The penguin uniformly accelerates during the entire time period. What is the net force exerted on the penguin?
To find the net force exerted on the penguin, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a), or F = m * a.
First, we need to find the acceleration of the penguin. We can use the formula for uniformly accelerated motion:
d = v_0 * t + 0.5 * a * t^2
Where:
d is the distance traveled (50.7 m)
v_0 is the initial velocity (0, as the penguin starts from rest)
t is the time taken (1.7 s)
a is the acceleration
Rearranging the formula, we get:
a = (2 * (d - v_0 * t)) / t^2
Plugging in the values:
a = (2 * (50.7 - 0 * 1.7)) / (1.7^2)
a = (2 * 50.7) / (2.89)
a ≈ 35.02 m/s^2
Now that we have the acceleration, we can calculate the net force using Newton's second law:
F = m * a
F = 13 kg * 35.02 m/s^2
F ≈ 455.26 N
Therefore, the net force exerted on the penguin is approximately 455.26 Newtons.
a = (final velocity-initial velocity) / time
a = (0 - Vi)/1.7
so a = -Vi/1.7
d = Vi t + (1/2) a t^2
50.7=Vi(1.7) -(1/2)(Vi/1.7)(1.7)^2
50.7 = (1/2)(1.7)Vi
Vi = 59.6 m/s
then
a = - Vi/1.7 = -35.1 m/s^2
so F = m a = 13(-35.1)
= - 456 N
Damon,
Thanks for answering my question. What I don't understand is why gravity is not an issue in this problem? Could you please explain?