newtons second law

calculating acceleration

The equation for acceleration given above can be used to calculate the acceleration of an object that is acted on by an unbalanced force. For example, assume you are pushing a large wooden trunk, like the one shown in Figure acceleration of the trunk, substitute these values in the equation for acceleration: a= F 20 N 2N = = m 10 kg kg Recall that one newton (1 N) is the force needed to cause a 1-kilogram mass to accelerate at 1 m/s2 . Therefore, force can also be expressed in the unit kgm/s2 . This way of expressing force can be substituted for newtons in the solution to the problem: a= 2 N 2 kg m/s2 = = 2 m/s2 kg kg Why are there no kilograms in the final answer to this problem? The kilogram units in the numerator and denominator of the fraction cancel out. As a result, the answer is expressed in the correct units for acceleration: m/s2 . You Try It! Problem: Assume that you add the weights to the trunk in Figure 14.7. If you push the trunk and weights with a force of 20 N, what will be the trunks acceleration? Need more practice? You can find additional problems at this URL:

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acceleration and weight

Newtons second law of motion explains the weight of objects. Weight is a measure of the force of gravity pulling on an object of a given mass. Its the force (F) in the acceleration equation that was introduced above: a= F m This equation can also be written as: F = ma The acceleration due to gravity of an object equals 9.8 m/s2 , so if you know the mass of an object, you can calculate its weight as: F = m 9.8 m/s2 As this equation shows, weight is directly related to mass. As an objects mass increases, so does its weight. For example, if mass doubles, weight doubles as well. You can learn more about weight and acceleration at this URL: Problem Solving Problem: Daisy has a mass of 35 kilograms. How much does she weigh? Solution: Use the formula: F = m 9.8 m/s2 . F = 35 kg 9.8 m/s2 = 343.0 kg m/s2 = 343.0 N You Try It! Problem: Daisys dad has a mass is 70 kg, which is twice Daisys mass. Predict how much Daisys dad weighs. Then calculate his weight to see if your prediction is correct. Helpful Hints The equation for calculating weight (F = m a) works only when the correct units of measurement are used. Mass must be in kilograms (kg). Acceleration must be in m/s2 . Weight (F) is expressed in kgm/s2 or in newtons (N).

acceleration force and mass

Newton determined that two factors affect the acceleration of an object: the net force acting on the object and the objects mass. The relationships between these two factors and motion make up Newtons second law of motion. This law states that the acceleration of an object equals the net force acting on the object divided by the objects mass. This can be represented by the equation: Net force , or Mass F a= m Acceleration = You can watch a video about how Newtons second law of motion applies to football at this URL: http://science36

direct and inverse relationships

Newtons second law shows that there is a direct relationship between force and acceleration. The greater the force that is applied to an object of a given mass, the more the object will accelerate. For example, doubling the force on the object doubles its acceleration. The relationship between mass and acceleration, on the other hand, is an inverse relationship. The greater the mass of an object, the less it will accelerate when a given force is applied. For example, doubling the mass of an object results in only half as much acceleration for the same amount of force. Consider the example of a batter, like the boy in Figure 14.6. The harder he hits the ball, the greater will be its acceleration. It will travel faster and farther if he hits it with more force. What if the batter hits a baseball and a softball with the same amount of force? The softball will accelerate less than the baseball because the softball has greater mass. As a result, it wont travel as fast or as far as the baseball.

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instructional diagrams

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questions

Which two factors have an inverse relationship?

a. force and acceleration

b. force and mass

c. mass and gravity

-->  d. mass and acceleration

Any change in the motion of an object is called

a. speed.

b. velocity.

c. direction.

-->  d. acceleration.

In the equation F = m a, if a is the acceleration due to gravity, what is F?

a. mass

-->  b. weight

c. friction

d. frequency

If you push a 20-kg box with a force of 10 N, what is its acceleration?

a. 20 m/s2

b. 10 m/s2

c. 2 m/s2

-->  d. 0.5 m/s2

Newton determined that the acceleration of an object depends on the net force acting on the object and the objects

a. size.

-->  b. mass.

c. weight.

d. velocity.

The relationship between mass and inertia is described by Newtons second law of motion.

a. true

-->  b. false

Newton determined that there is a direct relationship between force and mass.

-->  a. true

b. false

Any change in velocity for any reason is called acceleration.

-->  a. true

b. false

Newtons second law shows that there is a direct relationship between net force and acceleration.

-->  a. true

b. false

The greater the net force applied to a given object, the more it will accelerate.

-->  a. true

b. false

Doubling the mass of an object doubles its weight.

-->  a. true

b. false

The greater the mass of an object, the more it will accelerate when a given net force is applied to it.

a. true

-->  b. false

A net force of 1 N applied to a mass of 1 kg results in an acceleration of 0.5 m/s2 .

a. true

-->  b. false

Force can be expressed as kg m/s.

a. true

-->  b. false

Your weight equals your mass multiplied by the acceleration due to gravity.

-->  a. true

b. false

Any object that is accelerating is changing its speed.

a. true

-->  b. false

If a balanced force acts on an object, the object will accelerate.

a. true

-->  b. false

A 10-kg object has greater acceleration due to gravity than a 5-kg object.

a. true

-->  b. false

The acceleration of an object equals its mass times the net force applied to it.

a. true

-->  b. false

The acceleration of an object due to gravity depends on the objects initial velocity

a. true

-->  b. false

An object is accelerating when it

a. speeds up.

b. slows down.

c. changes direction.

-->  d. any of the above

Newtons second law of motion relates an objects acceleration to

a. its mass.

b. its velocity.

c. the net force acting on it.

-->  d. two of the above

Doubling the net force acting on an object

-->  a. doubles its acceleration.

b. decreases it acceleration.

c. cuts its acceleration in half.

d. does not affect its acceleration.

If you push a 20-kilogram mass with a force of 40 N, what will be the objects acceleration?

a. 40 m/s2

b. 20 m/s2

c. 10 m/s2

-->  d. 2 m/s2

Which units can be used to express force?

a. N

b. kg/s2

c. kg  m/s2

-->  d. two of the above

If you know the mass of an object, you can calculate its weight with the formula

a. F

b. F

-->  c. F

d. F

If the mass of an object doubles, its weight

-->  a. doubles.

b. decreases.

c. is not affected.

d. changes by a factor of 21 .

acceleration due to gravity

a. acceleration

b. weight

c. direct relationship

d. a =

e. inverse relationship

f. F = m  a

-->  g. 9.8 m/s2

formula for weight

a. acceleration

b. weight

c. direct relationship

d. a =

e. inverse relationship

-->  f. F = m  a

g. 9.8 m/s2

formula for acceleration

a. acceleration

b. weight

c. direct relationship

-->  d. a =

e. inverse relationship

f. F = m  a

g. 9.8 m/s2

measure of the force of gravity pulling on an object

a. acceleration

-->  b. weight

c. direct relationship

d. a =

e. inverse relationship

f. F = m  a

g. 9.8 m/s2

type of relationship between acceleration and mass

a. acceleration

b. weight

c. direct relationship

d. a =

-->  e. inverse relationship

f. F = m  a

g. 9.8 m/s2

measure of the change in velocity of a moving object

-->  a. acceleration

b. weight

c. direct relationship

d. a =

e. inverse relationship

f. F = m  a

g. 9.8 m/s2

type of relationship between acceleration and force

a. acceleration

b. weight

-->  c. direct relationship

d. a =

e. inverse relationship

f. F = m  a

g. 9.8 m/s2

diagram questions

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