An astronaut of mass 120 kg recedes from her spacecraft by activating a small propulsion unit attached to her back. The force generated by a spurt is 30 N. Show that her acceleration is 0.25 m/s2.
F = ma
30 = 120a
a = 30/120 = .25
Well, let's do some calculations here. We know that mass (m) times acceleration (a) equals force (F). So, if the force (F) applied by the propulsion unit is 30 N, and the mass (m) of the astronaut is 120 kg, we can set up the equation:
m * a = F
Substituting the given values:
120 kg * a = 30 N
Now let's isolate the acceleration. We divide both sides of the equation by the mass:
a = 30 N / 120 kg
Simplifying:
a = 0.25 N/kg
So, the acceleration is 0.25 N/kg, or 0.25 m/s². But hey, don't worry, she won't fly off into space – she's got her trusty propulsion unit keeping her grounded!
To show that her acceleration is 0.25 m/s², we can use Newton's second law of motion:
F = ma
Where:
F is the force exerted on the astronaut (30 N),
m is the mass of the astronaut (120 kg), and
a is the acceleration of the astronaut.
Rearranging the equation, we have:
a = F/m
Substituting the given values, we get:
a = 30 N / 120 kg
a = 0.25 m/s²
Therefore, the acceleration of the astronaut is 0.25 m/s².
To find the astronaut's acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula for Newton's second law is:
F = m * a
Where:
F is the net force acting on the object,
m is the mass of the object, and
a is the acceleration of the object.
In this case, the force generated by the propulsion unit is 30 N, and the mass of the astronaut is 120 kg. Plugging these values into the formula, we have:
30 N = 120 kg * a
To solve for a, divide both sides of the equation by the mass (120 kg):
a = 30 N / 120 kg
Now, divide the numerator (30) by the denominator (120):
a = 0.25 N/kg
The unit of acceleration is meters per second squared (m/s^2). Since 1 N/kg = 1 m/s^2, the acceleration of the astronaut is indeed 0.25 m/s^2.