# Friction on an incline 2 problems

1. Apr 2, 2004

### Polak

I've tired everything i can think of, anyone that can be of any help i would appriceate it.

A block with a mass of 5 kg is held in equilibrium on an incline of angle = 30.0° by the horizontal force, F, as shown in Figure 4-31. Find the magnitude of F.
( ) N
Find the normal force exerted by the incline on the block. (Disregard friction.)
( )N

and

A box of books weighing 209 N is shoved across the floor by a force of 500 N exerted downward at an angle of 35° below the horizontal.

(a) If µk between the box and the floor is 0.57, how long does it take to move the box 10 m, starting from rest? (If the box will not move, enter 0.)
[ ] s
(b) If µk between the box and the floor is 0.75, how long does it take to move the box 10 m, starting from rest?
[ ] s

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Last edited: Apr 2, 2004
2. Apr 2, 2004

### HallsofIvy

Staff Emeritus
Draw a "vector" (line segment) representing the horizontal force, F pointing to the incline. Set up a right triangle having that as hypotenuse, one leg perpendicular to the incline and one along it (you should see that one angle in the right triangle is 30 degrees). Use trigonometry to calculate the "components" of the force perpendicular to and along the incline in terms of F.

Now draw a vector (line segment) vertically representing the weight of the block (which is (5kg)(9.81m/s2)= 49.05 N) Again, draw a right triangle having that as hypotenuse and legs perpendicular to and along the incline. Use trigonometry to calculate the components of weight perpendicular to and along the incline.

The components of weight and F along the incline must have the same value (but opposite sign) so that the block does not move. Set them equal and solve for F. Once you know F, the component of F perpendicular to the incline is the "normal" force.

In the second problem, you know the coefficient of friction. That times the weight of the box is the friction force.

One more time, set up a right triangle having the force as hypotenuse and making angle 35 degrees to the floor. Use trigonometry to calculate the component of force parallel to the floor.

That force, minus the friction force, is the net force on the box. Once you have that use "F= ma" to find the acceleration and then use that to find the time necessary to move the box 10 m

3. Apr 3, 2004

### Polak

ah crap i had my calculator in radians not degrees, hence why whenever i input my answers into the "webassign" it wasn't right. Since it was due 11pm last night i think ill just stick my tail between my legs and run away.

4. Apr 3, 2004