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A force $\mathbf { F } = ( 10.0 \mathbf { i } + 9.0 \mathbf { j } + 12.0 \mathbf { k } ) \mathrm { kN }$ acts on a small object of mass 95$\mathrm { g } .$ If the displacement of the object is $\mathbf { d } = ( 5.0 \mathbf { i } + 4.0 \mathbf { j } ) \mathrm { m } ,$ find the work done by the force. What is the angle between $\vec { \mathbf { F } }$ and $\mathbf { d } ?$

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$$42^{\circ}$$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

03:47

In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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7.79. We have a force and a displacement that are given for some object a za massive 95 grams, which doesn't end up being relevant, but they tell us anyway. So we'd like to find the work that this force does over, uh, while causing this displacement of then what the angle is between the force into displacement. So the work is the dot product of the force and the displacement. Because the force is constant. Note that this is in units of killer Newton's. So the work is 86 killer Jules. Now, from basically the definition of not the definition necessarily. But from from this being a dot product, we also know that this is the magnitude of the two vectors multiplied by each other and by the coast sine of the angle between them. So angle be the Arco sign of the work, divided by the product of the magnitudes of the force into displacement. The force you can find pretty easily has a magnitude of 18 killer Newton's and the displacement has a magnitude of 6.4 meters. We've just found what the work is. So the angle between these two vectors is 42 degrees

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