"A moving object has a kinetic energy of 145 J and a momentum with a magnitude of 40.0 kg·m/s. Determine the mass and speed of the object."
I simply cannot figure it out. I know that KE=.5mv^2 and that p=mv but I can't seem to piece it together. Please explain?
40=mv
145=.5mv^2
divide the second equation by the first.
145/40=.5v
v=290/40 m/s
then figure m.
Thank you so much!
Sure! I can help you with this problem. To determine the mass and speed of the object, we can use both the kinetic energy (KE) and momentum (p) equations that you mentioned.
First, let's review the equations we need:
1. Kinetic energy (KE) = 0.5 * mass (m) * velocity (v)^2
2. Momentum (p) = mass (m) * velocity (v)
Now let's go ahead and solve the problem step by step:
Step 1: Given values:
- Kinetic energy (KE) = 145 J
- Momentum (p) = 40.0 kg·m/s
Step 2: Use the momentum equation to find the mass (m):
p = m * v
40.0 kg·m/s = m * v
Step 3: Rearrange the equation to solve for mass (m):
m = p / v
Step 4: Plug in the given values for momentum (p) and solve for mass (m):
m = 40.0 kg·m/s / v (equation A)
Step 5: Now, let's use the kinetic energy equation and substitute the expression for mass (m) from equation A:
KE = 0.5 * m * v^2
145 J = 0.5 * (40.0 kg·m/s / v) * v^2
Step 6: Simplify the equation:
145 J = 0.5 * 40.0 kg·m/s * v
290 J = 40.0 kg·m/s * v
Step 7: Solve for velocity (v):
v = 290 J / (40.0 kg·m/s)
Step 8: Calculate the numerical value of velocity (v):
v = 7.25 m/s
Step 9: Substitute the value of velocity (v) back into equation A to find the mass (m):
m = 40.0 kg·m/s / 7.25 m/s
Step 10: Calculate the numerical value of mass (m):
m ≈ 5.52 kg
So, the mass of the object is approximately 5.52 kg and the speed of the object is approximately 7.25 m/s.