Physics
Work and Energy
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#57 For a conservative force, the potential energy function $U$ satisfies:
A) $\nabla\times\vec F=\nabla U$
B) $\nabla\cdot\vec F=U$
C) $\vec F=-\nabla U$
D) $\vec F=+\nabla U$
#58 Energy stored in a spring stretched by $x$ is:
A) $kx$
B) $k/x$
C) $kx^2$
D) $\tfrac12 kx^2$
#59 For a conservative force, the potential energy function $U$ satisfies:
A) $\vec F=+\nabla U$
B) $\nabla\times\vec F=\nabla U$
C) $\nabla\cdot\vec F=U$
D) $\vec F=-\nabla U$
#60 The work–energy theorem for a particle of mass $m$ is:
A) $W_{\text{net}}=\Delta K$
B) $W_{\text{net}}=\Delta p$
C) $W_{\text{net}}=\Delta U$
D) $W_{\text{net}}=m\Delta v$
#61 For a conservative force, the potential energy function $U$ satisfies:
A) $\vec F=-\nabla U$
B) $\nabla\cdot\vec F=U$
C) $\vec F=+\nabla U$
D) $\nabla\times\vec F=\nabla U$
#62 Instantaneous power delivered by a constant force is:
A) $P=F^2v$
B) $P=\vec F\cdot\vec v$
C) $P=F/v$
D) $P=Fv\sin\theta$
#63 A constant force $F=20\,\text{N}$ acts through $s=10\,\text{m}$ at $\theta=90^\circ$. The work done is:
A) $0$
B) $Fs$
C) $F+s$
D) $F/s$
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