The students made it to the bottom with out a problem but added 400 kg for a total of 455 kg and slides for 12.2 s across the surface of a frozen lake. If the coefficient of kinetic friction between the kid and the ice is 0.071, what is the change in the students momentum as they comes to a stop? How far does the students slide before the ice breaks and are swallowed by a whale?
Z6654
To calculate the change in the student's momentum as they come to a stop, you first need to calculate their initial momentum and final momentum.
The initial momentum (p_initial) can be calculated using the mass of the student (m) and the initial velocity (v_initial). Since the students made it to the bottom without a problem, we can assume their initial velocity is zero. Therefore, the initial momentum is:
p_initial = m * v_initial
= 455 kg * 0 m/s
= 0 kg∙m/s
The final momentum (p_final) can be calculated using the concept of kinetic friction. The force of kinetic friction (F_friction) can be determined by multiplying the coefficient of kinetic friction (μ_k) by the weight of the student. The weight can be calculated by multiplying the mass (m) by the acceleration due to gravity (g = 9.8 m/s^2). Therefore, the force of kinetic friction is:
F_friction = μ_k * m * g
Using the force of kinetic friction, we can calculate the deceleration (a) of the student using Newton's second law of motion (F = ma):
F_friction = m * a
μ_k * m * g = m * a
a = μ_k * g
Since the student comes to a stop, the final velocity (v_final) is also zero. The final momentum is given by:
p_final = m * v_final
= 455 kg * 0 m/s
= 0 kg∙m/s
The change in momentum (Δp) is the difference between the initial and final momentum:
Δp = p_final - p_initial
= 0 kg∙m/s - 0 kg∙m/s
= 0 kg∙m/s
Therefore, the change in the student's momentum as they come to a stop is 0 kg∙m/s.
As for the second part of your question regarding how far the students slide before the ice breaks and they are swallowed by a whale, we don't have enough information to calculate that. The distance traveled by the students would depend on other factors such as the angle of the slide, the total acceleration, and the force applied by the students themselves.