A spaceship takes off vertically from rest with an acceleration of 25.5 m/s2. a) What magnitude of force f is exerted on a 56.0 kg astronaut during takeoff?
1428
b)Express f as a multiple the astronaut's weight w on Earth.
I was able to solve A but I have no clue how to do part b.
b) The magnitude of the force exerted on the astronaut during takeoff is 25.5 times the astronaut's weight on Earth.
Well, let's solve part B using some humor, shall we?
To express the force f as a multiple of the astronaut's weight w on Earth, we need to understand that on Earth, the astronaut is already feeling the force of gravity, which we know is equal to their weight. So, let's imagine the astronaut on Earth feeling the force of gravity saying, "Hey gravity, you're really pulling me down!"
Now, during takeoff, the force exerted on the astronaut is the force f. So let's imagine the astronaut during takeoff saying, "Hey force f, you're really pushing me up!"
In order to express f as a multiple of the astronaut's weight on Earth, let's compare these two forces. Imagine the astronaut looking at f and saying, "Hey f, you're pushing me up 1428 times stronger than gravity is pulling me down!"
So, the force f can be expressed as 1428 times the astronaut's weight on Earth.
Remember, physics can be fun if you add a little humor!
To solve part b, you need to find the weight of the astronaut on Earth and then express the force exerted during takeoff as a multiple of that weight.
The weight of an object can be found using the formula:
Weight = mass * gravitational acceleration
On Earth, the gravitational acceleration is approximately 9.8 m/s^2. So, the weight of the astronaut on Earth is:
Weight on Earth = mass * gravitational acceleration
= 56.0 kg * 9.8 m/s^2
= 548.8 N
To express the force exerted during takeoff as a multiple of the astronaut's weight on Earth, you divide the force (found in part a) by the weight on Earth:
f = Force exerted during takeoff = 1428 N
w = Weight on Earth = 548.8 N
Multiple = f / w
= 1428 N / 548.8 N
= 2.60 times (rounded to two decimal places)
So, the magnitude of the force exerted on the astronaut during takeoff is approximately 2.60 times the astronaut's weight on Earth.
To solve part b, we need to express the force (f) as a multiple of the astronaut's weight (w) on Earth. We know that weight is calculated using the formula:
w = m * g
where m is the mass of the astronaut and g is the acceleration due to gravity on Earth (approximately 9.8 m/s^2).
Since we are looking for f in terms of w, we need to find a ratio between the two quantities.
Let's go step-by-step:
1. Calculate the weight (w) of the astronaut on Earth using the formula: w = m * g
w = 56.0 kg * 9.8 m/s^2
w = 549.6 N
2. Now, we compare this weight (w) with the force (f) exerted during takeoff. The relationship between the force and weight can be expressed as a multiple, given by:
f = n * w
where n is the ratio or multiple we are trying to find.
3. To find n, we can rearrange the formula as:
n = f / w
4. Substitute the given value of force (f) and the calculated value of weight (w) into the formula:
n = 1428 N / 549.6 N
n ≈ 2.6
Therefore, the magnitude of force (f) exerted on the astronaut during takeoff is approximately 2.6 times the astronaut's weight (w) on Earth.