An object is moving so that its kinetic energy
is 198 J and the magnitude of its momentum
is 13
.
1 kg
·
m
/
s.
Determine the speed of the object.
Answer in units of m
/
s.
Eq1:0.5M*V^2 = 198 J.
Eq2: M*V = 13
M = 13/V
In Eq1, replace M with 13/V:
0.5*(13/V)*V^2 = 198
6.5*V = 198
V = 30.5 m/s.
To determine the speed of the object, we can use the equation for kinetic energy and the equation for momentum.
The equation for kinetic energy is given by:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
The equation for momentum is given by:
Momentum (p) = mass * velocity
Given that the kinetic energy (KE) is 198 J and the magnitude of momentum (p) is 13.1 kg·m/s, we can set up two equations as follows:
198 J = 1/2 * mass * velocity^2 ...........(equation 1)
13.1 kg·m/s = mass * velocity ...........(equation 2)
To solve for the speed, we need to eliminate the mass variable from these equations. To do that, we can solve equation 2 for mass:
mass = Momentum (p) / velocity
Substituting this into equation 1, we get:
198 J = 1/2 * (Momentum (p) / velocity) * velocity^2
Simplifying further:
198 J = 1/2 * (p) * velocity
Now, we can solve for velocity:
velocity = (2 * 198 J) / (p)
Substituting the given value of p = 13.1 kg·m/s into the equation:
velocity = (2 * 198 J) / (13.1 kg·m/s)
Calculating the result gives us:
velocity ≈ 30.15 m/s
Therefore, the speed of the object is approximately 30.15 m/s.