Chapter 8.4, Problem 24PSC

Solution

a.

To find the Angle between the two vectors.

The angle between the two vectors is ${67}^{\circ }$

Given: An object is placed on a ramp, part of its weight is directed along the ramp as a sliding force and $\text{w=50}$ .

Calculation: Here, angle between the two vectors is

${90}^{\circ }-{23}^{\circ }$

➔ ${67}^{\circ }$

Conclusion: Hence, the angle between the two vectors is ${67}^{\circ }$

b.

To find the value of f.

The value of “f” is $19.536$

Given: An object is placed on a ramp, part of its weight is directed along the ramp as a sliding force and $\text{w=50}$ .

Concept used: Here, we are using the formula,

$\text{wcosθ=f}$

Calculation: Here, the formula is

$\text{wcosθ=f}$

➔ ${\text{wcos67}}^{\text{o}}\text{=f}$

➔ ${\text{f=50cos67}}^{\text{o}}$

➔ $\text{f=19}\text{.536}$

Conclusion: Hence, the value of f is $19.536$