You have landed on an unknown planet, Newtonia, and want to know what objects will weigh there. You find that when a certain tool is pushed on a frictionless horizontal surface by a 12.2 N force, it moves 16.3 m in the first 2.30 s, starting from rest. You next observe that if you release this tool from rest at 10.6 m above the ground, it takes 2.68 s to reach the ground.
What does the tool weigh on Newtonia?
What would it weigh on Earth?
The average velocity after pushing 16.3 m is
V = 2*(16.3m/2.3s) = 14.17 m/s
F X = (1/2) M V^2
M = 2 F X/V^2
Solve for M. Then get the acceleration of gravity, g', on the planet from the second measurement
(1/2) g' t^2 = 10.6 m
Solve that for g'. It will be less than the value on Earth
The weight is M g' on Newtonia and M g on Earth
afdadf
Why is The average velocity after pushing V = 2*(16.3m/2.3s)
Where did u get the 2 from?
When x is known and here it is x = 16.3m we use the equation of motion for constant acceleration
Vx^2 = Vix^2 + 2Ax(x-xi) where
Vx is our velocity
Vix is our initial velocity
A is our acceleration or distance/time
x is our final point
and xi is our starting point
so to answer your question, the 2 is just part of the equation.
Whoa, slow down there, Captain Science! We're on Newtonia, not Science Land. So, let's put this in terms even a clown like me can understand.
On Newtonia, the tool would weigh M times g'. And on Earth, it would weigh M times g. Easy peasy!
But since I'm a clown and not a scientist, I don't have the magic formulas to calculate all that fancy stuff. So let's just say, on Newtonia, the tool would weigh whatever it weighs, and on Earth, it would weigh whatever it weighs too. Weight is a funny thing, it can change depending on where you are. So embrace your weight on whatever planet you're on and keep on clowning around!
To find the weight of the tool on Newtonia, we need to start by calculating its mass. We can use the equation F X = (1/2) M V^2, where F X is the applied force, M is the mass, and V is the average velocity.
From the given information, we know that the applied force is 12.2 N and the tool moves 16.3 m in 2.30 s. We can calculate the average velocity V by dividing the total distance travelled by the total time taken: V = 2*(16.3 m/2.3 s) = 14.17 m/s.
Substituting the values into the equation, we have 12.2 N = (1/2) M (14.17 m/s)^2. Solving for M, we get M = 2 * (12.2 N) / (14.17 m/s)^2.
Now, to determine the acceleration of gravity on Newtonia, denoted by g', we can use the second measurement. When the tool is released from rest at 10.6 m above the ground, it takes 2.68 s to reach the ground. We can use the equation (1/2) g' t^2 = 10.6 m, where t is the time taken to fall.
Plugging in the values, we have (1/2) g' * (2.68 s)^2 = 10.6 m. Solving for g', we find g' = (2 * 10.6 m) / (2.68 s)^2.
With the mass of the tool and the acceleration of gravity, we can calculate the weight of the tool on Newtonia using the formula Weight = M * g'. Similarly, on Earth, the weight would be given by the formula Weight = M * g, where g is the acceleration of gravity on Earth (approximately 9.8 m/s^2).
So, to summarize:
Weight on Newtonia = M * g'
Weight on Earth = M * g
The specific values can be calculated by substituting the known values into the equations obtained earlier.