In the movie Superman, Lois Lane falls from a building and is caught by the diving superhero. Assuming that Lois, with a mass of 45 kg, is falling at a terminal velocity of 56 m/s,
A)how much force does Superman exert on her if it takes 0.7 s to slow her to a stop?
B)If Lois can withstand a maximum acceleration of 7 g's, what minimum time should it take Superman to stop her after he begins to slow her down?
I know the answer for A is 4040 N but by doing mass time velocity over time I always seem to be off on my answer
To find the force exerted by Superman on Lois Lane, you can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the acceleration is the change in velocity over time (Δv / Δt).
A) To find the force exerted by Superman, you need to determine the change in velocity. Since Lois is falling at a terminal velocity, her velocity remains constant at 56 m/s until Superman slows her down. The change in velocity (∆v) is therefore 56 m/s (initial velocity) - 0 m/s (final velocity), which equals 56 m/s.
Since the time taken (∆t) to slow her down is given as 0.7 seconds, you can now calculate the acceleration (a) using the formula a = ∆v / ∆t. Plugging in the values, you get a = 56 m/s / 0.7 s = 80 m/s².
Finally, you can calculate the force (F) using Newton's second law, F = m * a. Plugging in the mass of Lois (m = 45 kg) and the acceleration (a = 80 m/s²), you get F = 45 kg * 80 m/s² = 3600 N.
However, this force only represents the force exerted by Superman to bring Lois to a stop. To find the total force exerted by Superman on Lois during this time, you need to consider the force required to counteract her weight as well. The weight (W) can be calculated using W = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s²).
The weight of Lois is W = 45 kg * 9.8 m/s² = 441 N. Since Superman must exert an equal and opposite force to counteract her weight, you need to add the weight to the force calculated earlier: F_total = F + W = 3600 N + 441 N = 4041 N (rounded to the nearest whole number).
Therefore, the force exerted by Superman on Lois Lane is approximately 4041 N.
B) To find the minimum time required for Superman to stop Lois if she can withstand a maximum acceleration of 7 g's, you need to determine the maximum acceleration that Lois can tolerate.
Since 1 g is equal to 9.8 m/s² (acceleration due to gravity), 7 g's would be 7 * 9.8 m/s² = 68.6 m/s².
Using the formula a = ∆v / ∆t, where a is the acceleration and ∆v is the change in velocity, you can rearrange the formula to solve for the ∆t (time taken). The equation becomes ∆t = ∆v / a.
In this case, the change in velocity (∆v) is the same as before, 56 m/s. Plugging in the values, ∆t = 56 m/s / 68.6 m/s² = 0.818 seconds (rounded to 3 decimal places).
Therefore, the minimum time it should take Superman to stop Lois after he begins to slow her down is approximately 0.818 seconds.