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 calculate the force exerted by Superman on Lois Lane, we 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 force exerted by Superman will be equal to the change in momentum of Lois Lane as he brings her to a stop.
A) To calculate the force exerted by Superman on Lois Lane, we first need to determine the initial momentum (p) of Lois Lane before she is caught by Superman. The formula for momentum is given by p = m*v, where m is the mass and v is the velocity.
Given:
Mass (m) = 45 kg
Velocity (v) = 56 m/s
Initial momentum (p1) = m * v
= 45 kg * 56 m/s
Next, we need to calculate the final momentum (p2) of Lois Lane after she is stopped by Superman. As she comes to a stop, her velocity will decrease to zero.
Final momentum (p2) = m * v
= 45 kg * 0 m/s
= 0 kg * m/s
The change in momentum (Δp) is the difference between the initial and final momenta.
Change in momentum (Δp) = p2 - p1
= 0 kg*m/s - (45 kg * 56 m/s)
= -2520 kg*m/s
The negative sign indicates that the direction of the momentum has changed.
Now, we can calculate the force exerted by Superman on Lois Lane using the formula F = Δp / t, where Δp is the change in momentum and t is the time taken to bring Lois Lane to a stop.
Given:
Change in momentum (Δp) = -2520 kg*m/s
Time (t) = 0.7 s
Force (F) = Δp / t
= -2520 kg*m/s / 0.7 s
= -3600 N
The negative sign suggests that the force exerted by Superman is in the opposite direction to the motion of Lois Lane. However, it is common to consider force as a vector quantity, so we can ignore the negative sign and simply state that the force exerted by Superman on Lois Lane is 3600 N.
B) To calculate the minimum time it should take Superman to stop Lois Lane while maintaining a maximum acceleration of 7 g's, we can use the formula a = Δv / t, where a is the acceleration, Δv is the change in velocity, and t is the time taken.
Given:
Maximum acceleration (a) = 7 g's = 7 * 9.8 m/s^2 (converting g's to m/s^2)
= 68.6 m/s^2 (approximately)
Change in velocity (Δv) = 56 m/s (terminal velocity)
Rearranging the formula, we have t = Δv / a.
Time (t) = 56 m/s / 68.6 m/s^2
= 0.816 s (approximately)
So, the minimum time it should take Superman to stop Lois Lane while maintaining a maximum acceleration of 7 g's is approximately 0.816 seconds.
To calculate the force that Superman exerts on Lois Lane, we 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 (Δv) divided by the time (t) it takes for that change to occur.
A) To find the force exerted by Superman when it takes 0.7 seconds to slow Lois Lane to a stop, we can start by calculating the change in velocity. The change in velocity is her initial velocity (56 m/s) minus her final velocity (0 m/s). Since she comes to a stop, the final velocity is 0 m/s.
Δv = 56 m/s - 0 m/s = 56 m/s
Next, we can calculate the acceleration using the formula:
a = Δv / t
Substituting the values we have:
a = 56 m/s / 0.7 s = 80 m/s²
Finally, we can find the force using Newton's second law:
F = m * a
Substituting the values of mass and acceleration:
F = 45 kg * 80 m/s² = 3600 N
Therefore, the answer for part A is 3600 N, not 4040 N. Please verify your calculations.
B) To find the minimum time it should take Superman to stop Lois Lane while considering her maximum acceleration tolerance of 7 g's (where 1 g = 9.8 m/s²), we can use a similar approach.
First, we need to convert 7 g's to meters per second squared:
a = 7 g * 9.8 m/s² = 68.6 m/s²
Now, we can use Newton's second law again to find the time:
F = m * a
Since we want to find the time (t), we can rearrange the formula as:
t = Δv / a
We already know the initial velocity (56 m/s), and the final velocity will be 0 m/s again, as Lois comes to a stop. Therefore:
Δv = 56 m/s - 0 m/s = 56 m/s
Substituting the values:
t = Δv / a = 56 m/s / 68.6 m/s² ≈ 0.82 s
Therefore, the minimum time Superman should take to stop Lois Lane, considering her maximum acceleration tolerance, would be approximately 0.82 seconds.