KnowledgeBoat Logo
|

Physics

Shan is utilising a dynamometer to measure the force, expressed in newtons, on a bowstring. He records both the force and displacement of the bowstring and plots the data on a graph that shows the relationship between force in newtons and displacement in centimetres. Shan is interested in determining the highest point that the arrow reaches. He knows he can calculate the work done by finding the area under the graph.

Shan is utilising a dynamometer to measure the force, expressed in newtons, on a bowstring. Physics Competency Focused Practice Questions Class 10 Solutions.

(a) What is the potential energy stored in the bow string, when the force is 25 N?

(b) If the mass of the arrow is 31.25 g, calculate the maximum velocity attained by the arrow.

(c) Calculate the maximum height reached by the arrow.

Work, Energy & Power

1 Like

Answer

(a) PE = work done =area under the graph = 12\dfrac{1}{2} x b x h = 12\dfrac{1}{2} × 25 x 0.05 = 0.625 J

(b) Given, mass of arrow = 31.25 g = 0.03125 kg

By law of conservation of energy,

PE of the bow string = KE of the arrow

0.625 J=12×0.03125×vmax2vmax=0.625×20.03125vmax=40vmax=6.32 ms−10.625 \text { J} = \dfrac{1}{2}\times 0.03125\times \text {v}{max}^2 \\[1em] \text v{max} = \sqrt{\dfrac{0.625\times 2}{0.03125}} \\[1em] \text v{max} = \sqrt{40} \\[1em] \text v{max} = 6.32 \text{ ms}^{-1} \\[1em]

So, the maximum velocity attained by the arrow is 6.32 ms-1

(c) The potential energy stored in the bow string = mghmax\text {mgh}_{max}

hmax=0.6250.03125×10hmax=0.6250.3125hmax=2 m\text h{max} =\dfrac{0.625}{0.03125\times 10}\\[1em] \text h{max} =\dfrac{0.625}{0.3125}\\[1em] \text h_{max} = 2\text{ m}\\[1em]

So, the maximum height attained by the arrow is 2 m

Answered By

1 Like

Related Questions