Question

The torque of an engine's crankshaft varies with time as shown. What is the approximate angular impulse the engine provides from 1.0 to 1.5 seconds?

Answer 1

Given a torque-time graph.

The angular impulse can be calculated as the product of the torque and the time. The angular impulse can be found from a torque-time graph by calculating the area under the curve just like we calculate impulse from a force-time graph.

The area under the curve in the interval 1.0 s to 1.5 s forms a triangle.

From the graphy, the approximate height of the triangle is h=10 Nm

The approximate base of the triangle is b=1.5-1.0=0.5 s

The area of a triangle is given by,

`A=(1)/(2)* b* h`

On substituting the known values,

`\begin{gathered} A=(1)/(2)*0.5*10 \\ =2.5\text{ N}\cdot\text{ m}\cdot\text{ s} \\ \approx3\text{ N}\cdot\text{ m}\cdot\text{ s} \end{gathered}`

Thus the approximate angular impulse provided by the engine is 3 N·m·s

Therefore the correct answer is option 5.