just 2 more problems

[swimmer3]

A 10-pound weight is lying on a sit-up bench at the gym. If the bench is inclined at an angle of 13 degrees, there are three forces acting on the weight. N is called the normal force and it acts in the direction perpendicular to the bench. F is the force due to friction that holds the weight on the bench. If the weight does not move, then the sum of these three forces is 0. Find the magnitude of N and the magnitude of F.

I foung that the magnitude of F=2.2 lb. How do I find the magnitude of N?




Also, Mark pulls Allison and Mattie in a wagon by exerting a force of 30 pounds on the handle at an angle of 21 degrees with the horizontal. How much work is done by Mark in pulling the wagon 220 feet?

Is this correct? If not how do I do this?
(30cos21)(220)=6161 ft/lb

 

[mmm4444bot]

… I found that the magnitude of F = 2.2 lb. How do I find the magnitude of N?

I'm thinking that it's simply the length of the other leg of the right triangle that you used to find 2.2 (i.e., the component of the gravity vector that is equal and opposite to N).

… Is this correct? … (30cos21)(220)=6161 ft/lb

Yup. Except that it's not rounded properly.

Also, cosine is a function. Please use function notation.

30 cos(21°) (220) = 6162 ft/lb

 

[swimmer3]

When I figure the magnitude of N that way I get 10.2. The only options given to me are 9.7 or 5.1. Which is it?

For the second problem I get 6162, but the answer options are: 6,200ft, 6,400ft, 6,000ft, 6,500ft, or 6,300ft. Which would that be?

 

[mmm4444bot]

|N| = 10 cos(13°) = 9.7437

|F| = 10 sin(13°) = 2.2495

They're probably enforcing rules for significant figures, so everything needs to be reported to two significant digits.

Round 6162 to the nearest hundred, to express two significant digits.

 

[Denis]

6101 to 6149 = 6100
6150 to 6199 = 6200