Tiger Woods can hit a golf ball quite hard. A golf ball just after being hit by Mr. Woods has a kinetic energy of 100 J and a momentum of 3 kg m/s. What is the mass of the golf ball in grams?
KE = 1/2 times mass times velocity squared
45 GRAMS
To find the mass of the golf ball in grams, we'll first convert the given momentum from kg m/s to g cm/s, and then use the formula for kinetic energy to solve for mass.
Let's start by converting the momentum from kg m/s to g cm/s.
1 kg = 1000 g (since 1 kg = 1000 grams)
1 m = 100 cm (since 1 meter = 100 centimeters)
So, to convert kg m/s to g cm/s, we can multiply the given momentum by the conversion factors:
3 kg m/s * (1000 g / 1 kg) * (1 m / 100 cm) = 300 g cm/s
Now, let's use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the kinetic energy is 100 J and the momentum is 300 g cm/s, we can rearrange the formula to solve for mass:
100 J = (1/2) * mass * (velocity)^2
Since velocity is given in cm/s, we can rewrite the equation as:
100 J = (1/2) * mass * (300 cm/s)^2
Simplifying further:
100 J = (1/2) * mass * 90000 cm^2/s^2
Dividing both sides of the equation by 90000 cm^2/s^2:
100 J / 90000 cm^2/s^2 = (1/2) * mass
Now we can solve for the mass by multiplying both sides of the equation by 2:
2 * (100 J / 90000 cm^2/s^2) = mass
Therefore, the mass of the golf ball is:
mass = (2 * 100 J) / (90000 cm^2/s^2)
mass ≈ 0.0022 g
So, the mass of the golf ball is approximately 0.0022 grams.