Two objects have the same kinetic energy. One has a speed that is 3.0 times greater than the speed of the other. What is the ratio of their masses? (Let m1 be the slower object and m2 be the faster.)
m1/m2=
To find the ratio of their masses, we can use the formula for kinetic energy:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
Since both objects have the same kinetic energy, we can set up the following equation:
(1/2) * m1 * v1^2 = (1/2) * m2 * v2^2
Given that the speed of the faster object (v2) is 3.0 times greater than the speed of the slower object (v1), we can write:
v2 = 3v1
Substituting this into the equation, we get:
(1/2) * m1 * v1^2 = (1/2) * m2 * (3v1)^2
Simplifying further:
m1 * v1^2 = m2 * 9v1^2
Dividing both sides by v1^2:
m1 = m2 * 9
To find the ratio of their masses, we divide both sides by m2:
m1/m2 = 9
Therefore, the ratio of their masses (m1/m2) is 9.
To find the ratio of their masses, let's go step by step:
First, let's denote the mass of the slower object as m1 and the mass of the faster object as m2.
Given that both objects have the same kinetic energy, we can set up the following equation:
(1/2) * m1 * v1^2 = (1/2) * m2 * v2^2
Here, v1 represents the speed of the slower object, and v2 represents the speed of the faster object.
Since we know that the speed of the faster object is 3.0 times greater than the speed of the slower object (v2 = 3.0 * v1), we can substitute v2 in terms of v1:
(1/2) * m1 * v1^2 = (1/2) * m2 * (3.0 * v1)^2
Simplifying the equation:
m1 * v1^2 = m2 * (9.0 * v1^2)
Dividing both sides of the equation by v1^2:
m1 = m2 * 9.0
Now, we can express the ratio of the masses:
m1/m2 = 1/9
Therefore, the ratio of their masses is 1/9.
nvm, i got all these answers..
1/9
(1/2) m1 V1^2 = (1/2)(m2)(3^2 V1^2)
m1/m2 = 9