In the outer space, a constant force is applied to a 32.5 kg probe initially at rest. The probe moves a distance of 100 m in 10 s.
(a) What acceleration does this force produce?
(b) What is the magnitude of the force?
This doesn't make since could you elaborate on how you get one half
(a) Well, to find the acceleration, we can use the equation of motion: distance equals initial velocity multiplied by time plus one-half the acceleration multiplied by time squared. In this case, we are given the initial velocity as zero, so the equation simplifies to distance equals one-half the acceleration multiplied by time squared. Plugging in the values, we get 100 m = (1/2) a (10 s)^2. Solving for acceleration, we find that it is 2 m/s^2. So, the force produces an acceleration of 2 m/s^2.
(b) Now, to find the magnitude of the force, we can use Newton's second law of motion, which states that force equals mass multiplied by acceleration. Plugging in the given mass of 32.5 kg and the calculated acceleration of 2 m/s^2, we get force = 32.5 kg * 2 m/s^2 = 65 N. Therefore, the magnitude of the force is 65 Newtons.
So, the acceleration is 2 m/s^2 and the magnitude of the force is 65 N. And you thought outer space was just a bunch of empty nothingness! It's full of physics fun!
To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
(a) To find the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Since the probe is initially at rest, its initial velocity is zero. The final velocity can be calculated using the formula:
final velocity = initial velocity + acceleration * time
In this case, the probe moves a distance of 100 m in 10 s, so the final velocity can be calculated as follows:
final velocity = 100 m / 10 s = 10 m/s
Now we can calculate the acceleration by substituting the values into the formula:
acceleration = (10 m/s - 0 m/s) / 10 s
= 10 m/s / 10 s
= 1 m/s²
Therefore, the acceleration produced by the force is 1 m/s².
(b) To find the magnitude of the force, we can use the formula:
force = mass * acceleration
In this case, the mass of the probe is given as 32.5 kg, and the acceleration is 1 m/s². Substituting the values into the formula, we can calculate the magnitude of the force:
force = 32.5 kg * 1 m/s²
= 32.5 N
Therefore, the magnitude of the force applied to the probe is 32.5 Newtons.
To find the acceleration produced by the force in outer space and the magnitude of the force, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
(a) To find the acceleration, we can use the formula:
acceleration = (change in velocity) / (time taken)
In this case, the probe is initially at rest, so the change in velocity is equal to the final velocity. As there is no information given about the final velocity, we can use the formula for velocity:
velocity = (distance traveled) / (time taken)
Using the given values, we have:
distance traveled = 100 m
time taken = 10 s
Substituting these values into the equation, we get:
velocity = 100 m / 10 s = 10 m/s
So, the acceleration is:
acceleration = (change in velocity) / (time taken) = (10 m/s) / (10 s) = 1 m/s²
Therefore, the acceleration produced by the force is 1 m/s².
(b) To find the magnitude of the force, we can use the formula:
force = mass * acceleration
Using the given values:
mass = 32.5 kg
acceleration = 1 m/s²
Substituting these values into the equation, we get:
force = 32.5 kg * 1 m/s² = 32.5 N
Therefore, the magnitude of the force applied to the probe is 32.5 N.
d = (1/2) a t^2
100 = (1/2) a (100)
so
a = 2 m/s^2
F = m a = 32.5*2 = 65 N