Chapter 1: Q8E (page 195)

A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force $\vec{F} = (30 N) \hat{i} ‐ (40 N) \hat{j}$ to the cart as it undergoes a displacement $\vec{s} = (‐ 9.0 m) \hat{i} ‐ (3.0 m) \hat{j}$ . How much work does the force you apply do on the grocery cart?

Short Answer

Expert verified

The total work applied by constant force to the grocery cart is -150 J.

Step by step solution

Identification of the given data

The given data is listed below as-

The magnitude of the force acting on the cart is, $\vec{F} = (30 N) \hat{i} ‐ (40 N) \hat{j}$
The displacement is, $\vec{s} = (- 9.0 m) \hat{i} ‐ (3.0 m) \hat{j}$

Significance of the work done on a particle by a constant force

Work done on a particle by a constant force $\vec{F}$ during a linear displacement $\vec{s}$ is given by

$W = \vec{F} \cdot \vec{s}$ ………….(1)

Determination of work applied by constant force to the grocery cart

The work done can be obtained using equation (1), such that

For, $\vec{F} = (30 N) \hat{i} - (40 N) \hat{j}$ and $\vec{s} = (- 9.0 m) \hat{i} - (3.0 m) \hat{j}$

The total work done will be

$W = (F_{x} \hat{i} + F_{y} \hat{j}) \cdot (s_{x} \hat{i} + s_{y} \hat{j}) = F_{x} s_{x} + F_{y} s_{y} = (30 N \times - 9 m) + (- 40 N \times - 3 m) = - 150 N \cdot m W = - 150 J$

The total work applied by constant force to the grocery cart is -150 J.

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Short Answer

Step by step solution

Identification of the given data

Significance of the work done on a particle by a constant force

Determination of work applied by constant force to the grocery cart

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A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force F→=(30N)i^‐(40N)j^to the cart as it undergoes a displacement s→=(‐9.0m)i^‐(3.0m)j^. How much work does the force you apply do on the grocery cart?

Short Answer

Step by step solution

Identification of the given data

Significance of the work done on a particle by a constant force

Determination of work applied by constant force to the grocery cart

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Rotational Dynamics

Modern Physics

Energy Physics

Physics of Motion

Electrostatics

Study anywhere. Anytime. Across all devices.