A billiard ball of mass 159 g is about to collide with another stationary ball. It has 2.4 J of kinetic energy. What is its speed? Give your answer to one decimal place.

Question

BlackTom AI · Accepted Answer

Question restatement: A billiard ball of mass 159 g is about to collide with another stationary ball. It has 2.4 J of kinetic energy. What is its speed? Give your answer to one decimal place.

Step 1: Convert mass to kilograms, since kinetic energy is typically computed with SI units. 159 g = 0.159 kg.

Step 2: Recall the kinetic energy formula: KE = 1/2 m v^2, where KE is the kinetic energy, m is mass, and v is speed.

Step 3: Solve for v: v = sqrt(2 * KE / m).

Step 4: Plug in the numbers: v = sqrt(2 * 2.4 J / 0.159 kg) = sqrt(4.8 / 0.159).

Step 5: Compute the quotient: 4.8 / 0.159 ≈ 30.19.

Step 6: Take the square root: sqrt(30.19) ≈ 5.495… m/s.

Step 7: Round to one decimal place as required: v ≈ 5.5 m/s.

Common pitfalls to avoid: ensure mass is converted to kilograms; use the correct rearrangement of the KE formula (don’t misplace the 1/2 or misapply KE = m v^2); verify the arithmetic when dividing 4.8 by 0.159 and when taking the square root, as small errors can affect the final rounded value.

If you’re checking your work, you can also rearrange the expression as v^2 = 2 KE / m, compute v^2 first, then take the square root, which should align with the steps above.

A billiard ball of mass 159 g is about to collide with another stationary ball. It has 2.4 J of kinetic energy. What is its speed? Give your answer to one decimal place.数值题

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