An object has a kinetic energy of 304 J and a momentum of magnitude 26.7 kg · m/s.
(a) Find the speed of the object.
(b) Find the mass of the object.
To find the speed of the object, we can use the formula for kinetic energy:
Kinetic energy = (1/2) * m * v^2
where m is the mass of the object and v is its speed.
Let's denote the speed of the object as v and the mass of the object as m.
(a) We are given that the kinetic energy is 304 J. Therefore, we can write:
304 = (1/2) * m * v^2
To find the speed v, we need to rearrange the equation:
v^2 = (2 * kinetic energy) / m
Now, we need to find the mass of the object.
(b) We are given that the momentum of the object has a magnitude of 26.7 kg · m/s. Momentum is defined as the product of mass and velocity, so we can write:
Momentum = m * v
Substituting the given values, we have:
26.7 = m * v
Now we have two equations:
1) v^2 = (2 * kinetic energy) / m
2) 26.7 = m * v
We can solve these equations simultaneously to find the values of v and m.
Here is a step-by-step solution:
1) v^2 = (2 * kinetic energy) / m
Rewrite the equation as:
v^2 = 2 * kinetic energy / m
Substitute the given values:
v^2 = 2 * 304 J / m
2) 26.7 = m * v
Solve for v:
v = 26.7 / m
Substitute this value for v in equation 1:
(26.7 / m)^2 = 2 * 304 J / m
Square both sides to eliminate the square:
712.89 / m^2 = 2 * 304 J / m
Rearrange terms:
712.89 / m^2 - 2 * 304 J / m = 0
Multiply through by m^2 to get a quadratic equation:
712.89 - 2 * 304 J * m = 0
Simplify:
712.89 - 608 J * m = 0
Solve for m:
608 J * m = 712.89
m = 712.89 / 608 J
Now substitute the value of m back into equation 2 to find the speed:
v = 26.7 / m
v = 26.7 / (712.89 / 608 J)
a) (304/26.7)*2 = 22.8
b) 26.7/22.8 = 1.173