A 3.00 kg toy falls froma height of 1.00m. What will the kinetic energy of the toy be just before it hits the ground. No air resistance and g=9.81m/s
Amswers: 0.98J
9.8 J
29.4 J
294 J
I used the formula 1/2 m times v^2
3. times 9.8^2/2 =144. Please help-what am I doing wrong?
This is a trick question. THe amount of gravitational potential energy stored at the top has to equal the final KEnergy.
GPE = mgh= 3kg*9.8*1= 29.4J
Now, for folks who are gluttons for punishment, we can do it that way.
what is the velocity from falling?
Vf^2=Vi^2+2gd= 2*9.8*1= 19.6
Vf= sqrt (19.6)
KE= 1/2 m v^2= 1/2 *3*19.6= 3/2 19.6=29.4J
Well, it seems like you forgot to include the potential energy of the toy before it fell. Remember, when an object falls, it converts its potential energy into kinetic energy. In this case, the potential energy is given by the equation PE = mgh, where m is the mass (3.00 kg), g is the acceleration due to gravity (9.81 m/s²), and h is the height (1.00 m).
So, the potential energy of the toy is:
PE = (3.00 kg) × (9.81 m/s²) × (1.00 m) = 29.43 J
Now, to calculate the kinetic energy just before the toy hits the ground, you can subtract the potential energy from the total mechanical energy. The total mechanical energy is conserved, so we have:
Total mechanical energy = Potential energy + Kinetic energy
Since the toy is falling from rest, it starts with no kinetic energy. Therefore:
Total mechanical energy = Potential energy
Now, if we substitute the values we calculated:
Total mechanical energy = 29.43 J
So, the correct answer is 29.4 J. Looks like someone dropped the ball, and it wasn't the toy!
To calculate the kinetic energy of the toy just before it hits the ground, you need to consider the potential energy it initially has due to its height.
The formula for potential energy is given by: PE = mgh, where m is the mass (3.00 kg), g is the acceleration due to gravity (9.81 m/s^2), and h is the height (1.00 m).
So, the potential energy at the height is: PE = (3.00 kg)(9.81 m/s^2)(1.00 m) = 29.43 J.
The potential energy will be converted entirely to kinetic energy just before the toy hits the ground, so the kinetic energy will also be 29.43 J.
Therefore, the correct answer is 29.4 J.
To calculate the kinetic energy of an object, you are correct in using the formula:
Kinetic Energy (KE) = 1/2 * m * v^2
Where:
m = mass of the object
v = velocity of the object
In this case, the mass of the toy is 3.00 kg. However, you need to find the velocity of the toy just before it hits the ground.
To find the velocity, you can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (which is what we need to find)
u = initial velocity (which is 0 in this case, as the toy falls from rest)
a = acceleration (which is equal to the acceleration due to gravity, g, since there is no air resistance)
s = distance traveled (which is the height the toy falls, 1.00m in this case)
Plugging in the values:
v^2 = 0^2 + 2 * 9.81 * 1.00
v^2 = 19.62
v ≈ 4.43 m/s
Now that you have the velocity (v ≈ 4.43 m/s), you can calculate the kinetic energy using the formula:
KE = 1/2 * m * v^2
KE = 1/2 * 3.00 * (4.43)^2
KE = 0.5 * 3.00 * 19.62
KE ≈ 29.4 J
Therefore, the correct answer to this question is 29.4 J.