Rate, Distance, and Time Problems, 7

Category: Physics, Mechanics

"Published in Newark, California, USA"

A motorist has to travel 3.50 km in a city where his average speed should not exceed 25 km/hr. If he increases his average speed to 40 km/hr, how much time will he gain in his journey?

Solution:

The given problem is about rate, distance, and time problem in which the average speed is increased. Let's assume that the distance for the two cases is the same which is 3.50 km. 

If the speed limit in a city is 25 km/hr, then his travel time is

If he increased his speed to 40 km/hr, then his travel time is
 

 

 

 

Therefore, his travel time will gain by
 

 

 

                         or

 

Inclined Plane Problems, 3

Category: Mechanics, Physics

"Published in Newark, California, USA"

The block shown in the figure is acted on by its weight W = 400 lbs., a horizontal force F = 600 lbs., and the pressure P exerted by the inclined plane. The resultant R of these forces is parallel to the incline. Determine P and R. Does the block move up or down the incline?

Photo by Math Principles in Everyday Life

Solution:

The first thing that we need to do is to get the x and y components of each forces and then isolate the given figure as follows 

Photo by Math Principles in Everyday Life

Since we don't know the direction of the resultant, let's assume that the direction is upward because the value of F is greater than the weight of a block. 

The sum of x component is

The sum of y component is

Substitute the value of P to the first equation. Therefore, the value of R is

Since the value of R is positive, then the block is moving upward the incline. 
 

Resultant of Forces and Components, 2

Category: Mechanics, Physics

"Published in Newark, California, USA"

The force system as shown in the figure has a resultant of 200 lbs. pointing up along the y axis. Compute the values of F and θ required to give this resultant.

Photo by Math Principles in Everyday Life

Solution:

The first thing that we need to do is to get the x and y components of each forces and then isolate the given figure as follows

Photo by Math Principles in Everyday Life

The sum of y components is

The sum of x components is

 

 

 

 

Divide the first equation by the second equation in order to solve for θ, we have
 

Take the inverse tangent on both sides on the equation, we have

                                or

Substitute the value of θ to either of the two working equations, we have