A moving object has a kinetic energy of 188 J and a momentum with magnitude of 26.2 kg·m/s.
Determine the mass of the object.
To determine the mass of an object based on its kinetic energy and momentum, you can use the formulas for kinetic energy and momentum.
The formula for kinetic energy (KE) is:
KE = (1/2) * m * v^2
where m is the mass of the object and v is its velocity.
The formula for momentum (p) is:
p = m * v
where m is the mass of the object and v is its velocity.
In this case, you are given the kinetic energy (188 J) and the magnitude of the momentum (26.2 kg·m/s).
Step 1: Determine the velocity of the object.
To find the velocity, you can rearrange the momentum formula:
p = m * v
v = p / m
Given that the magnitude of the momentum is 26.2 kg·m/s, and you are looking for the magnitude of the velocity, use the magnitude of the momentum as it is:
v = 26.2 kg·m/s
Step 2: Substitute the velocity into the kinetic energy formula.
Now that you know the velocity, you can substitute it into the kinetic energy formula:
KE = (1/2) * m * v^2
Given that the kinetic energy is 188 J, and the magnitude of the velocity is 26.2 kg·m/s, substitute the values:
188 J = (1/2) * m * (26.2 kg·m/s)^2
Simplify the equation and solve for m:
376 J = m * (26.2 kg·m/s)^2
Step 3: Solve for the mass.
To solve for the mass, divide both sides of the equation by (26.2 kg·m/s)^2 and then take the square root of both sides:
m = √(376 J / (26.2 kg·m/s)^2)
Using a calculator, calculate the square root of (376 J / (26.2 kg·m/s)^2) to find the mass.
The mass of the moving object is the answer you obtain from the calculation.