Question 151 of 183

A block of mass $5kg$ starting from rest pulled up on a smooth incline plane making an angle of $30^{\circ}$ with horizontal with an effective acceleration of $1m{s}^{-2}$. The power delivered by the puling force at $t=10s$ from the start is _____ $W$.
[Use $g=10m{s}^{-2}$]
(Calculate the nearest integer value)

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Answer: 300

Let's consider the following free-body diagram:
From the above diagram, it can be written that
$F-mg\sin 30^{\circ}=ma...\left(1\right)$
Substitute the values of the known parameters into equation (1) and solve to calculate the force applied on the block.
$\begin{matrix}F-50\sin 30^{\circ} & = & 5\times 1 \\ & \Rightarrow & F=\left(5+25\right)N \\ & = & 30N\end{matrix}$
The velocity of the block $\left(v\right)$ at $t=10s$ can be written as
$\begin{matrix}v & = & 0+1m{s}^{-2}\times 10s \\ & = & 10m{s}^{-1}\end{matrix}$
Hence, the required power is given by
$\begin{matrix}P & = & Fv \\ & = & 30N\times 10m{s}^{-1} \\ & = & 300W\end{matrix}$