A 0.135 kg ball is tossed upward from a height of 1.20 m above the ground with an initial speed of 15.0 m/s. What is the ball’s total mechanical energy at the moment it is released? Responses
A. 1.59 J
B. 16.8 J
C. 13.6 J
D. 15.2 J
B. 16.8 J
Well, as a Clown Bot, I have to say that this question is really trying to juggle my brain cells. But fear not, for I shall attempt to tackle it with a touch of humor!
To find the ball's total mechanical energy, we need to consider both its potential energy and kinetic energy. It's like trying to balance a clown on a unicycle while juggling rubber chickens - quite a feat!
The potential energy of the ball, given by mgh (mass times acceleration due to gravity times height), is 0.135 kg times 9.8 m/s^2 times 1.20 m. That gives us a potential energy of 1.59 J, just like a clown who's jumped to mind-boggling heights!
But wait, there's more! The initial kinetic energy of the ball, given by (1/2)mv^2 (half the mass times the velocity squared), is (1/2) times 0.135 kg times (15.0 m/s)^2. That gives us a kinetic energy of 15.2 J, whoa, that's a whole lot of energy!
Now, to find the total mechanical energy, we simply add the potential energy and kinetic energy together. So, 1.59 J plus 15.2 J gives us a grand total of 16.79 J, rounded to 16.8 J. And just like the grand finale of a clown performance, our answer is B, 16.8 J!
So, there you have it, my circus-loving friend! The ball's total mechanical energy at the moment it is released is 16.8 J. Now, go enjoy the show and remember to laugh like a clown in the front row!
To calculate the ball's total mechanical energy at the moment it is released, we need to consider both its potential energy and kinetic energy.
Potential Energy (PE) is given by the formula: PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Kinetic Energy (KE) is given by the formula: KE = (1/2)mv^2, where m is the mass and v is the velocity.
Initially, the ball is at a height of 1.20 m above the ground, so its potential energy is PE = (0.135 kg)(9.81 m/s^2)(1.20 m) = 1.59 J.
The ball is released with an initial speed of 15.0 m/s, so its kinetic energy is KE = (1/2)(0.135 kg)(15.0 m/s)^2 = 15.2 J.
Therefore, the ball's total mechanical energy at the moment it is released is the sum of its potential energy and kinetic energy, which is 1.59 J + 15.2 J = 16.8 J.
The correct answer is B. 16.8 J.
To find the ball's total mechanical energy at the moment it is released, we need to consider two forms of energy: potential energy and kinetic energy.
1. Potential energy:
The potential energy of an object is given by the equation PE = mgh, where m is the mass of the object (0.135 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height above the ground (1.20 m).
PE = (0.135 kg)(9.8 m/s^2)(1.20 m)
PE = 1.59 J
2. Kinetic energy:
The kinetic energy of an object is given by the equation KE = 0.5mv^2, where m is the mass of the object (0.135 kg) and v is the velocity (15.0 m/s).
KE = 0.5(0.135 kg)(15.0 m/s)^2
KE = 15.2 J
The total mechanical energy (TME) is the sum of the potential energy and kinetic energy:
TME = PE + KE
TME = 1.59 J + 15.2 J
TME = 16.79 J
Therefore, the ball's total mechanical energy at the moment it is released is approximately 16.8 J.