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Clueless_2

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- Homework Statement
- A golfer strikes a 50 gram golf ball with a 225 gram clubhead travelling at 30 m/s. After impact the clubhead is travelling at 18 m/s. (iii) What is the initial velocity of the golf ball?

- Relevant Equations
- F dt = dp (p = momentum, d = change / difference)

p = mv

total p initial = total p final

I have done the first two parts of this question.

(i) Find the clubhead's change of momentum. ( dp = p_f - p_i = (0.225*18 - 0.225*30) = -2.7 kg ms^-1 )

(ii) Find the impulse given to the golf ball. (F dt = dp = 2.7 Ns from part (i) with just a change in the units. Because of the conservation of momentum, the reduction of the clubhead's momentum comes with an increase in the ball's momentum)

(iii) What is the initial velocity of the golf ball?

At first appearances, there seems to be two unknowns and only one equation. The velocity of the golf-ball, initial and final, are not specified explicitly. The only equation is the total initial momentum equals the final momentum. So I made two different assumptions and checked the logic and the answers.

Assumption 1: The golf ball is initially stationary. But this seems to makes this question trivial, since no work was needed to get to the answer. The answers (no worked solutions) begged to differ as well, stating the initial velocity was 54 ms^-1.

Assumption 2: The golf ball's final velocity is the same as the clubhead, since the question did not say they came apart after the impact. Then ...

(initial p of clubhead) + (initial p of ball) = (final p of clubhead) + (final p of ball)

0.225*30 + 0.05*v_i,b = 0.225*18+0.05*18 (where v_i,b is the initial speed of the golf ball)

6.75+ 0.05*v_i,b = 4.05+0.9

0.05*v_i,b = 4.95-6.75

v_i,b = -1.8 / 0.05

v_i,b = -36 m/s

So the initial velocity is -36 m/s, which means the golf ball was initially going in the opposite direction the clubhead was travelling. This seems unlikely, and once again it doesn't match the back-of-the-book answer of 54 ms^-1.

So i am veritably stuck ... for now.

lingering thoughts: I am wondering whether there is another equation that I missed? Because then I can solve for the two unknowns without making assumptions about the initial and final velocity of the golf ball.

Credits: Andrew Baylis & Gary McPhee et. al. 1994, Physics Study Guide Units 3 & 4, Longman Chesire Pty Ltd

(i) Find the clubhead's change of momentum. ( dp = p_f - p_i = (0.225*18 - 0.225*30) = -2.7 kg ms^-1 )

(ii) Find the impulse given to the golf ball. (F dt = dp = 2.7 Ns from part (i) with just a change in the units. Because of the conservation of momentum, the reduction of the clubhead's momentum comes with an increase in the ball's momentum)

(iii) What is the initial velocity of the golf ball?

At first appearances, there seems to be two unknowns and only one equation. The velocity of the golf-ball, initial and final, are not specified explicitly. The only equation is the total initial momentum equals the final momentum. So I made two different assumptions and checked the logic and the answers.

Assumption 1: The golf ball is initially stationary. But this seems to makes this question trivial, since no work was needed to get to the answer. The answers (no worked solutions) begged to differ as well, stating the initial velocity was 54 ms^-1.

Assumption 2: The golf ball's final velocity is the same as the clubhead, since the question did not say they came apart after the impact. Then ...

(initial p of clubhead) + (initial p of ball) = (final p of clubhead) + (final p of ball)

0.225*30 + 0.05*v_i,b = 0.225*18+0.05*18 (where v_i,b is the initial speed of the golf ball)

6.75+ 0.05*v_i,b = 4.05+0.9

0.05*v_i,b = 4.95-6.75

v_i,b = -1.8 / 0.05

v_i,b = -36 m/s

So the initial velocity is -36 m/s, which means the golf ball was initially going in the opposite direction the clubhead was travelling. This seems unlikely, and once again it doesn't match the back-of-the-book answer of 54 ms^-1.

So i am veritably stuck ... for now.

lingering thoughts: I am wondering whether there is another equation that I missed? Because then I can solve for the two unknowns without making assumptions about the initial and final velocity of the golf ball.

Credits: Andrew Baylis & Gary McPhee et. al. 1994, Physics Study Guide Units 3 & 4, Longman Chesire Pty Ltd