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202209270930 Exercise 5.3.B (Q1-Q6)

1. What is the potential energy of a 10\,\mathrm{kg} mass 25 metres above the ground?
2. A 3\,\mathrm{kg} mass is 20\,\mathrm{m} above the ground. How much potential energy does it have?
3. How high must you raise a 25\,\mathrm{kg} mass before it has a potential energy of 8500\,\mathrm{J}?
4. How high must you raise a 2\,\mathrm{kg} mass before it has a potential energy of 10\,\mathrm{J}?
5. A mass has a potential energy of 1000\,\mathrm{J} when it is 40\,\mathrm{m} above ground level. What is the mass?
6. A mass has a potential energy of 20\,\mathrm{J} when it is 50\,\mathrm{cm} above ground level. What is the mass?

Extracted from B. Kennedy. (1999). Progressive Problems for ‘S’ Grade Physics.

Background.

\textrm{PE}=mgh

Roughwork.

1.

\begin{aligned} \textrm{PE} & = mgh \\ & = (10)(9.81)(25) \\ & = 2450\,\mathrm{J}\qquad \textrm{(3 s.f.)} \\ \end{aligned}

2.

\begin{aligned} \textrm{PE} & = mgh \\ & = (3)(9.81)(20) \\ & = 589\,\mathrm{J}\qquad \textrm{(3 s.f.)} \end{aligned}

3.

\begin{aligned} \textrm{PE} & = mgh \\ 8500 & = (25)(9.81)(h) \\ h & = 34.7\,\mathrm{m}\qquad \textrm{(3 s.f.)} \end{aligned}

4.

\begin{aligned} \textrm{PE} & = mgh \\ 10 & = (2)(9.81)(h) \\ h & = 51.0\,\mathrm{cm}\qquad \textrm{(3 s.f.)} \end{aligned}

5.

\begin{aligned} \textrm{PE} & = mgh \\ 1000 & = (m)(9.81)(40) \\ m & = 2.55\,\mathrm{kg}\qquad \textrm{(3 s.f.)} \end{aligned}

6.

\begin{aligned} \textrm{PE} & = mgh \\ 20 & = (m)(9.81)(0.5) \\ m & = 4.08\,\mathrm{kg}\qquad \textrm{(3 s.f.)} \end{aligned}