# Forces

The **mass** of an object is a measure of the inertia of that object. **Inertia** is the tendency of a body at rest to remain at rest, and of the body in motion to continue moving with constant velocity.

Force, in general is what tries to cause change. In mechanics, it is a push or pull that changes the velocity of an object. Force is a vector quantity because it has magnitude and direction. An external force is one that lies outside of the system being considered. The net or resultant external force acting on an object causes the object to accelerate in the direction of that force. The acceleration is proportional to the force and inversely proportional to the mass of the object. The Newton is the SI unit of force. One **Newton** (1N) is that resultant force which will give a 1 kg mass an acceleration of 1 m/s2. One pound is 4.45 N.

### Newton's Laws

**Newton's First Law**: An object at rest will remain at rest and an object in motion will continue in motion with constant velocityunless acted upon by an external force. Force is what changes motion.

**Newton's Second Law**: If the resultant or net force acting on an object of mass is not zero, the object accelerates in the direction of the force. The acceleration is proportional to the force and inversely proportional to the mass of the object. With force in Newtons, mass in kilograms, and acceleration in m/s2, this can be written as:

**F = ma**

The acceleration has the same direction as the resultant force.

**Newton's Third Law**: Matter interacts with matter - forces come in pairs. For each force exerted on one body, there is an equal, but oppositely directed, force on some another body interacting with it. This is also called the **Law of Action and Reaction**.

The Law of Universal Gravitation: When two masses gravitationally interact, they attract each other with forces of equal magnitude. For point masses (or spherically symmetric bodies), the attractive force FG is given by:

The Law of Universal Gravitation: When two masses gravitationally interact, they attract each other with forces of equal magnitude. For point masses (or spherically symmetric bodies), the attractive force FG is given by:

**FG = G mm'/m2**

r = distance between mass centers

**G = 6.67 X 10-13 N m2/kg2** when FG is in Newtons, masses are in kilograms, and r is in meters.

The weight (FW) of an object is the gravitational force acting downward on the object. For objects close to the Earth's surface, the acceleration of gravity is "little g" or 9.8 m/s2. Therefore, F = FW = ma = mg. The SI unit for weight is expressed in Newtons. The units of kilogram, pounds, etc. are actually for mass, not weight. Thus, an object weighs less on the moon but has the same mass as the same object on Earth.

**Types of Forces**

The **tensile force** acting on a string, chain, tendon or other objects is the applied force tending to stretch it. The magnitude of the tensile force is the **tension**.

The **normal force** on an object that is being supported by a surface is the component of the supporting force that is perpendicular to the surface.

The **friction force** is a tangential force acting on an object that opposes the sliding of that object on an adjacent surface with which it is in contact. The friction force is parallel to the surface and opposite to the direction of motion or of impending motion. Only when the applied force exceeds the maximum static friction force will an object begin to move.

The **coefficient of static friction** (µk) is:

friction force (Ff) / normal force (FN)

The **coefficient of static friction** (µs) is:

max. friction force (Ff max) /normal force (FN) where the maximum friction force occurs when the object is just on the verge of slipping but is still at rest.

**Review Questions**:

1. Richard's car has a mass of 2200 kilograms. (a) What is his car's weight in Newtons? (b) What is the car's mass in pounds? (c) What is the car's weight on the moon which has a gravitational force 1/6th that of the Earth? (d) What is the car's mass on the moon?

a. 21,560 N

b. 4847 pounds

c. 3,593 kg

d. Mass does not change. It is the same.

2. Chris gets on an elevator at one of the hotels and pushes the button for the 25th floor. He is standing on a weight scale which reads 145 lbs. As the elevator begins to move upward, the scale reads 165 lbs. As the elevator reaches a constant velocity, the scale returns to 145 lbs. When the elevator slows, the scale reads 125 lbs. (a) What is the force on Chris produced by the elevator? (b) What is Chris's mass? (c) What is the acceleration of the elevator?

a. 89 N

b. 65.8 kg

c. 1.35 m/s2

3. Jocelyn wakes up late one morning and just can't bear the thought of missing her physics class so, she jumps in her car and accelerates from rest and reaches a speed of 60 mph in 6.0 seconds. The mass of the car is 1600 kg. What is the magnitude of the force that acts on the car?

7152 N

4. David's tool box tips over on a table and falls on his hand. The tool box weighs 10 lbs. What is the force on the top of his hand and what is the force on the bottom of his hand?

There is an equal force on the top and bottom of the hand!

5. Eugene gets a new stereo for his room because he gets a good grade in physics class. He tries to slide the box along the ground by pushing it. He pushes down and horizontally on the box, applying a force of 282 N at an angle of 20° below the horizontal. The box has a mass of 100 kg. The coefficient of static friction between the box and the floor is 0.25. Is he able to move the box? (Hint: draw a diagram showing angles. Normal force can be found by using 282 N x sin20°; horizontal pushing force on the box can be found by using 282 N x cos20°)

No. Fx is less than Fsso he is not pushing hard enough to overcome the force of static friction.