Chapter 1: Q13DQ (page 194)

A net force acts on an object and accelerates it from rest to speed V₁. In doing so, the force does an amount of work W₁. By what factor must the work done on the object be increased to produce three times the final speed, with the object again starting from rest?

Short Answer

Expert verified

The work done on the object will increased by a factor of 9 .

Step by step solution

About work energy theorem

The total work done is given by:

$W_{tot} = K_{2} ‐ K_{1} = ∆ K$

When forces act on a particle while it undergoes a displacement, the particle’s kinetic energy changes by an amount equal to the total work done on the particle by all the forces.

Determination of the total work done

The total work done using work energy theorem is given by,

$W_{t o t} = K_{2} ‐ K_{1} = ∆ K$

The Kinetic energy is 0 initially.

$K_{i n i t i a l} = 0$

Therefore, role="math" localid="1663745789333" $W_{t o t} = K_{f i n a l}$

Thus, $W_{t o t} = \frac{1}{2} m {V^{2}}_{f i n a l}$

Determination of the factor

The work done is given by,

$W_{1} = \frac{1}{2} m {V^{2}}_{1} W_{2} = \frac{1}{2} m {V^{2}}_{2}$

Now, the speed is increased 3 times

Therefore, $V_{2} = 2 V_{1}$

Work is proportional to the square of the speed,

So, $W_{2} = 9 W_{1}$

Thus, the work should be done nine times to produce three times the final speed and hence the factor is 9 .

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A net force acts on an object and accelerates it from rest to speed V₁. In doing so, the force does an amount of work W₁. By what factor must the work done on the object be increased to produce three times the final speed, with the object again starting from rest?

Short Answer

Step by step solution

About work energy theorem

Determination of the total work done

Determination of the factor

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A net force acts on an object and accelerates it from rest to speed V1. In doing so, the force does an amount of work W1. By what factor must the work done on the object be increased to produce three times the final speed, with the object again starting from rest?

Short Answer

Step by step solution

About work energy theorem

Determination of the total work done

Determination of the factor

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Conservation of Energy and Momentum

Wave Optics

Rotational Dynamics

Energy Physics

Electromagnetism

Study anywhere. Anytime. Across all devices.

A net force acts on an object and accelerates it from rest to speed V₁. In doing so, the force does an amount of work W₁. By what factor must the work done on the object be increased to produce three times the final speed, with the object again starting from rest?