On a planet far, far away, an astronaut picks up a rock. The rock has a mass of 4.20 kg, and on this particular planet its weight is 40.0 N. If the astronaut exerts an upward force of 45.5 N on the rock, what is its acceleration?
Magnitude
Well, if the astronaut is exerting an upward force greater than the weight of the rock, then the rock must be accelerating upwards. It's really defying gravity! Maybe it's a magical rock? But let's not get too carried away.
To find the acceleration, we can use Newton's second law, which states that force equals mass times acceleration. Since the astronaut is exerting an upward force of 45.5 N and the mass of the rock is 4.20 kg, we can set up the equation:
45.5 N = 4.20 kg * acceleration
Now we just solve for acceleration:
acceleration = 45.5 N / 4.20 kg
And when we do the math, we get:
acceleration ≈ 10.83 m/s²
So, the rock's acceleration is approximately 10.83 meters per second squared in the upward direction. Maybe it's not magic after all, just some good old-fashioned physics at work!
To find the acceleration, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.
The given information is:
Mass of the rock (m) = 4.20 kg
Weight of the rock (Fg) = 40.0 N
Upward force exerted by the astronaut (F) = 45.5 N
To find the acceleration (a), we can rearrange the formula:
F = m * a
In this case, the net force (F) acting on the rock is the difference between the upward force exerted by the astronaut and the weight of the rock:
F = F - Fg
Substituting the values:
F = 45.5 N - 40.0 N
F = 5.5 N
Now, substituting the values into the rearranged formula, we get:
5.5 N = 4.20 kg * a
To solve for a, divide both sides of the equation by the mass:
a = 5.5 N / 4.20 kg
Calculating the result:
a ≈ 1.31 m/s²
Therefore, the rock has an acceleration of approximately 1.31 m/s².
To find the acceleration of the rock, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
The equation for Newton's second law is:
F = ma
Where:
F = net force applied to the object
m = mass of the object
a = acceleration of the object
In this scenario, the net force applied to the rock is the difference between the upward force exerted by the astronaut and the weight of the rock.
Net force (F) = Upward force - Weight
Given:
Upward force = 45.5 N
Weight = 40.0 N
Mass (m) = 4.20 kg
So, the net force can be calculated as follows:
Net force = 45.5 N - 40.0 N
Net force = 5.5 N
Now, we can use Newton's second law to find the acceleration:
5.5 N = 4.20 kg * a
Dividing both sides of the equation by the mass (4.20 kg), we get:
a = 5.5 N / 4.20 kg
Using a calculator, we can find:
a ≈ 1.31 m/s^2
Therefore, the magnitude of the acceleration of the rock is approximately 1.31 m/s^2.
m*g = 40 N.
4.20g = 40
g = 9.52 m/s^2
a = F/m = 45.5/4.20 = 10.83 m/s^2.