IB Physics SL A.3.7 Mechanical energy conservation

Practise solving speed, height and stored-energy questions by conserving total mechanical energy when losses are negligible.

Exam points

apply mgh = 1/2 mv^2 to show a speed from a vertical drop, with clear substitution and units in m s^-1
include rotational KE when an object rolls without slipping, using I and ω with translational KE in one equation
find elastic energy from total mechanical energy by subtracting the kinetic part at a stated instant or position

[Maximum number: 2]

A student strikes a tennis ball that is initially at rest so that it leaves the racquet at a speed of $64 \mathrm{~m} \mathrm{~s}^{-1}$ . The ball has a mass of 0.058 kg and the contact between the ball and the racquet lasts for 25 ms .

The student strikes the tennis ball at point P . The tennis ball is initially directed at an angle of $7.00^{\circ}$ to the horizontal.

Figure for Question A.3.7—Mechanical energy conservation question 1 — IB Physics SL

The following data are available.

Table for Question A.3.7—Mechanical energy conservation question 1 — IB Physics SL

Determine the speed of the tennis ball as it strikes the ground.

ALTERNATIVE 1

Initial KE+PE= final KE /
$\frac{1}{2} \times 0.058 \times 64^{2}+0.058 \times 9.81 \times 2.80=\frac{1}{2} \times 0.058 \times v^{2}$

ALTERNATIVE 2
$\begin{aligned} & v_{v}=<\sqrt{7.8^{2}+2 \times 9.81 \times 2.8}>=10.8<\mathrm{ms}^{-1} \gg & <v=\sqrt{63.5^{2}+10.8^{2}}> & v=64.4<\mathrm{ms}^{-1} \gg \end{aligned}$

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A.3.7—Mechanical energy conservation question 1