# Statics: Finding Force Exerted and Reaction

A small hoist is mounted on the back of a pickup truck and is used to lift a 12kg crate. Determine (a) the force exerted on the hoist by the hydraulic cylinder BC, (b) the reaction at A.

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#### Solution Preview

First angle ACB = 90 -30 -15 = 45

So AC = 0.4*sin 15 /sin 45 = ...

#### Solution Summary

Trigonometry is used to solve for forces. The force exerted and reactions in static are determined.

Friction: Basic questions

1 Observe and Find a Pattern

Examine the data in the table that follows:

Mass of the block Surface area Quality of surfaces Maximum static friction force

1 kg 0.1 m2 Medium smooth 3.1 N

1 kg 0.2 m2 Medium smooth 3.0 N

1 kg 0.3 m2 Medium smooth 3.1 N

1 kg 0.1 m2 A little rougher 4.2 N

1 kg 0.1 m2 Even rougher 5.1 N

1 kg 0.1 m2 Roughest 7.0 N

a) Now decide how the maximum static friction force that the surface exerts on the block depends on the surface area of the block and on the roughness of the two surfaces.

3 Observe and Find a Pattern

Examine the data in the table that follows.

Mass of the block Extra downward force exerted on the 1-kg block Normal force exerted by the board on the block Maximum

static friction force

1 kg 0 N 10 N 3 N

1 kg 5 N 15 N 4.5 N

1 kg 10 N 20 N 6 N

1 kg 20 N 30 N 9 N

a) Use the data in the table to find the relationship between the maximum static friction force and the normal force the surface exerts on the block.

b) Express mathematically a relationship between the normal force and the maximum static friction force. Write this relationship as an equation.

4 Represent and Reason

Some students are trying to move a GIANT pumpkin across the room. Angelique pulls it across the floor at the same time that Gunnar and Jalen pull on it from the other side. Gunnar pulls on the pumpkin, exerting a (-150-N) force, and Jalen pulls exerting a (-125-N) force. There is also a (-200-N) friction force exerted by the floor on the pumpkin. The sum of the forces exerted on the desk is (+27-N).

a) Make a sketch of the situation.

b) Draw a force diagram for the pumpkin. Draw a motion diagram.

c) Write an algebraic statement that describes the force diagram you drew.

d) How hard is Angelique pulling?

e) Is the pumpkin moving with a constant velocity or is it speeding up? How do you know?

5 Represent and Reason

A 50-kg box of candy rests on the floor. The coefficients of static and kinetic friction between the bottom of the box and the floor are 0.70 and 0.50, respectively.

a) What is the minimum force a person needs to exert on it to start the box sliding?

b) After the box starts sliding, the person continues to push it exerting the same force. What is the acceleration of the box?

9 Represent and Reason Olympic skier Lindsey Vonn skis down a steep slope that descends at an angle of 30O below the horizontal. The coefficient of sliding friction between her skis and the snow is 0.10. Determine Vonn's acceleration, and her speed 6.0s after starting.

10 Represent and Reason

Bode Miller, 80-kg downhill skier, descends a slope inclined at 20O. Determine his acceleration if the coefficient of friction is 0.10. How would this acceleration compare to that of a 160-kg skier going down the same hill?