In the absence of air resistance, a ball of mass m is tossed upward to reach a height of 20m. Given that Fg=mg, what is the net force on the ball at the 10m position (half way up)?
a)2mg b)mg c)mg/4 d)mg/2
I already got this wrong bc I had no idea how to solve. I have a midterm coming up & I'm worried about a similar question, can someone show me step by step how I should have solved for that?
Thanks a ton!! :)
the net force on the ball is only from gravity, mg. Remember, even half way upwards, it is still accelerating downward due to the force of gravity.
the ball is in free fall with no air resistance
gravity is the only force on the ball
net force is ... m g
Ok, so then is it fair to say that when Fapp releases an object in the air or on a horizontal surface Fnet= the opposing force?
Thanks :)
Sure, I'd be happy to help you understand how to solve this problem step by step.
To find the net force on the ball at the 10m position, we need to understand the forces acting on the ball. In this case, the two main forces are:
1. The force due to gravity (Fg): This force pulls the ball downwards and is equal to the product of the mass of the ball (m) and the acceleration due to gravity (g).
2. The force exerted by the ball to reach the height of 10m.
Since the ball is tossed upward, the direction of the force exerted by the ball to reach the 10m position is opposite to that of the force due to gravity. Let's call this force F.
At the 10m position, the net force on the ball is the vector sum of these two forces: Fnet = F - Fg.
Since we know that Fg = mg, we can substitute this into the equation: Fnet = F - mg.
To solve for F, we need to use the principle of conservation of mechanical energy. In the absence of air resistance, the sum of kinetic and potential energy remains constant throughout the motion.
At the 10m position, the ball has zero velocity since it stops briefly before changing direction. This means that all of the initial kinetic energy is converted into potential energy.
Using the equation for potential energy, we can write: gravitational potential energy (PE) = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height above the reference point.
At the 10m position, the potential energy is given by PE = mgh = mg(10) = 10mg.
Since the initial kinetic energy is zero and the potential energy is 10mg, the total mechanical energy at the 10m position is 10mg.
Now, we can substitute the value of Fnet and total mechanical energy into the equation: Fnet = F - mg = 10mg - mg = 9mg.
Therefore, the net force on the ball at the 10m position is 9mg. So, the correct answer is (a) 2mg.
I hope this explanation helps you understand the problem and how to solve it. Good luck with your midterm! Let me know if you have any further questions.