A moving object has a kinetic energy of 146 J and a momentum of 23.4 kg·m/s.
a) Find the speed of the object. Answer in units of m/s.
.5 m v^2 = 146 = .5 mv v
m v = 23.4
so
146 = .5 (23.4) v
v = 146/11.7
To find the speed of the object, we need to use two formulas: one for kinetic energy and one for momentum. The formulas are:
1. Kinetic energy (KE) = (1/2)mv^2
2. Momentum (p) = mv
Given that the object has a kinetic energy of 146 J and a momentum of 23.4 kg·m/s, we can set up the following equations:
1. 146 = (1/2)m(v^2)
2. 23.4 = mv
From equation 2, we can solve for m (mass):
m = p/v
Substituting the value of momentum (p = 23.4 kg·m/s) and rearranging the formula:
23.4 = mv
m = 23.4 / v
Now, substituting this value of m into equation 1:
146 = (1/2)(23.4 / v)(v^2)
Simplifying this equation, we get:
146 = (11.7/v)(v^2)
146 = 11.7v
Dividing both sides of the equation by 11.7:
v = 146 / 11.7
Calculating this, we find:
v ≈ 12.47 m/s
Therefore, the speed of the object is approximately 12.47 m/s.