Superman rushes to save Lois Lane, who has fallen (has been pushed?) from a window 120 m above a crowded street. Superman swoops down in the nick of time, arriving when Lois is 2.0 m above the street and stopping her just at ground level. Lois has a mass of 65 kg. Ignore air resistance throughout.
(a) What is the impulse that Lois receives as Superman catches her?
Magnitude
__________kg¡Pm/s Direction
up/down
(b) If the force that Superman supplies in stopping Lois is constant, how long does it take for Lois to come to rest?
________s
(c) What is the average force Superman applies to Lois?
Magnitude
________N Direction
down/up
Compare this to the force of gravity on her.
________✕ mg
Someone please help!!!! I solved part (a) but no clue how to do the rest.
To solve the remaining parts of the problem, we will need to use the principles of physics, specifically those related to motion, force, and impulse.
(b) To find the time it takes for Lois to come to rest, we can use the equation that relates force, mass, and acceleration. In this case, acceleration can be calculated using the formula:
acceleration = final velocity / time
However, in this scenario, Lois comes to rest, meaning her final velocity is zero. Therefore, the equation becomes:
acceleration = 0 / time
acceleration = 0
Since acceleration is zero, we can conclude that Lois comes to rest with uniform motion (i.e., she decelerates uniformly). This implies that the net force acting on her must also be zero.
From Newton's second law, we know that force (F) is equal to mass (m) multiplied by acceleration (a):
F = m * a
Since acceleration is zero, the force is also zero. Therefore, it takes an infinite amount of time for Lois to come to rest. Superman must provide a continuously decreasing force to gradually reduce Lois's velocity to zero.
(c) To calculate the average force Superman applies to Lois, we can use the impulse-momentum theorem. The impulse (J) is the change in momentum and is equal to the force applied multiplied by the time for which it acts.
J = F * Δt
In this case, the impulse is equal to the change in momentum of Lois as Superman catches her. Since the final velocity is zero, the initial momentum (p) of Lois can be calculated using the equation:
p = mass * initial velocity
Given that Lois has a mass of 65 kg and the initial velocity is unknown, we need to find it. To determine Lois's initial velocity, we can use the equation of motion:
v^2 = u^2 + 2as
Where v is the final velocity, u is the initial velocity, a is acceleration, and s is the displacement. In this case, the displacement is the distance from the window to the point where Superman catches Lois.
The equation becomes:
0 = u^2 + 2as
To find the displacement, we need to calculate the total distance travelled by Lois:
total distance = distance fallen + distance stopped
The distance fallen is given as 120 m, and the distance stopped is given as 2.0 m. Therefore:
total distance = 120 m + 2.0 m
Substituting these values into the equation for displacement, we find:
120 m + 2.0 m = u^2
From here, solve for the initial velocity (u).
Once we have the initial velocity (u), we can calculate the initial momentum (p).
Finally, knowing the impulse (J) and initial momentum (p), we can calculate the force (F) Superman applies using the impulse-momentum theorem.
To compare this force to the force of gravity on Lois, multiply her mass (m) by the acceleration due to gravity (g), where g is approximately 9.8 m/s^2.
I hope this explanation helps you solve the remaining parts of the problem!