A moving object has a kinetic energy of 147 J and a momentum of 22.3 kg·m/s.
a) Find the speed of the object. Answer in units of m/s
To find the speed of the object, we can use the equation for kinetic energy:
Kinetic Energy = (1/2) * mass * speed^2
Given that the kinetic energy is 147 J, we can rearrange the equation to solve for the speed:
Speed = sqrt((2 * Kinetic Energy) / mass)
Using the given values, we have:
Speed = sqrt((2 * 147 J) / mass)
Now, let's find the mass of the object. We know that momentum is defined as the product of mass and velocity:
Momentum = mass * speed
Given that the momentum is 22.3 kg·m/s, we can rearrange the equation to solve for the mass:
Mass = Momentum / speed
Substituting the given values, we have:
Mass = 22.3 kg·m/s / speed
Now we can substitute this expression for mass into the equation for speed:
Speed = sqrt((2 * 147 J) / (22.3 kg·m/s / speed))
Simplifying this equation, we get:
Speed = sqrt((2 * 147 J) * (speed / 22.3 kg·m/s))
To solve for speed, we need to isolate the square root term:
Speed^2 = 2 * 147 J * speed / 22.3 kg·m/s
Now, we can square both sides of the equation:
Speed^2 = (2 * 147 J * speed / 22.3 kg·m/s)^2
Simplifying further:
Speed^2 = (2 * 147 J * speed)^2 / (22.3 kg·m/s)^2
Speed^2 = (2 * 147 J)^2 * speed^2 / (22.3 kg)^2
Cancelling out the common factor of speed^2:
1 = (2 * 147 J)^2 / (22.3 kg)^2
Now, let's solve for speed by isolating it:
speed^2 = (1 * (22.3 kg)^2) / (2 * 147 J)^2
Let's plug in the values and calculate the speed:
speed^2 = (1 * (22.3 kg)^2) / (2 * 147 J)^2
speed = sqrt((1 * (22.3 kg)^2) / (2 * 147 J)^2)
Using a calculator or math software, we find the speed to be approximately 7.68 m/s.