22ndnd Law Law

The force exerted by an The force exerted by an object is equal to its mass object is equal to its mass times its acceleration.times its acceleration.

F=maF=ma

22ndnd Law Law

5.2 The Second Law:Force, Mass, and Acceleration

:What is the mathematical

relationship between force, mass, and acceleration?

1. A 2kg object exerts a force of 10N. Calculate its acceleration.

F = 10 N or kg m/s2

m = 2 kg a = ?F = maRearrange equation to find a=?a = F = 10 kg m/s2

m 2a = 5 m/s²

2. An object with a mass of 2kg has an acceleration of 5 m/s2, Calculate the force exerted by the object.

m = 2 kg a = 5 m/s² F = ?F = maNo need to rearrange equation F = 2kg x 5m/s² = 10 N

3. An object with an acceleration of 10 m/s2 exerts a force of 10 N. Calculate its mass. F = 10 N or (kg m/s2) a = 10 m/s² m = ?F = maRearrange equation to find m =?m = F = 10 N a 10 m/s2

m = 1 kg

WE DOWE DO

1. 1. What acceleration will result What acceleration will result when a 12 N net force is when a 12 N net force is applied to a 3 kg object?applied to a 3 kg object?

  

““We do”We do”

1. F = 12 N1. F = 12 N m = 3 kgm = 3 kg a = ?a = ?

F = maF = maRearrange equation to find a =?Rearrange equation to find a =?a = a = F F = = 12 N 12 N = 4 m/s = 4 m/s²² m 3 kgm 3 kg

  

““We do”We do”

2. A net force of 16 N causes 2. A net force of 16 N causes an object to accelerate at a an object to accelerate at a rate of 5 m/srate of 5 m/s22. Calculate the . Calculate the mass of the object.mass of the object.

  

““We do”We do”

2. F = 16 N2. F = 16 N a = 5 m/sa = 5 m/s22

m = ?m = ?

F = maF = maRearrange equation to find m =?Rearrange equation to find m =?m = m = F F = = 16 N 16 N = 3.2 kg = 3.2 kg a 5 m/sa 5 m/s22

  

““We do”We do”

3. How much force is needed to 3. How much force is needed to accelerate a 66 kg skier at 1 accelerate a 66 kg skier at 1 m/sm/s22??

““We do”We do”

3. F = ?3. F = ? m = 66 kgm = 66 kg a = 1 m/sa = 1 m/s22

F = ma Direct substitution:F = ma Direct substitution:

F = ma = 66kg x 1m/sF = ma = 66kg x 1m/s²² = 66N= 66N

  

““We do”We do”

4. What is the force on a 1000 4. What is the force on a 1000 kg elevator that is falling freely kg elevator that is falling freely at 9.8 m/sat 9.8 m/s22??

““We do”We do”

4. F = ?4. F = ? m = 1000 kgm = 1000 kg a = 9.8 m/sa = 9.8 m/s22

F = maF = maDirect substitution:Direct substitution:F = ma = 1000kg x 9.8m/sF = ma = 1000kg x 9.8m/s²² = 9800 N= 9800 N

  

““We do”We do”

5. What is the acceleration of a 5. What is the acceleration of a 1400 kg car when a force of 2800 1400 kg car when a force of 2800 N is applied.N is applied.

““We do”We do”

5. F = 2800 N5. F = 2800 N m = 1400 kgm = 1400 kg a = ?a = ?

F = maF = maRearrange equation to find a =?Rearrange equation to find a =?a = a = F F = = 2800 N 2800 N = 2 m/s = 2 m/s22

m 1400 kgm 1400 kg

  

Newton’s 2nd Law proves that different masses accelerate to the earth at the same rate, but with different forces.

We know that objects with different masses accelerate to the ground at the same rate.

However, because of the 2nd Law we know that they don’t hit the ground with the same force.

F = maF = ma

98 N = 10 kg x 9.8 m/s/s98 N = 10 kg x 9.8 m/s/s

F = maF = ma

9.8 N = 1 kg x 9.8 9.8 N = 1 kg x 9.8 m/s/sm/s/s

Comparing the Mass of a dropped object and the size of the impact crater

Amount of sinkers

Mass of Container (g)

Depth of impact crater

(mm)

Diameter of impact crater

(mm)

RANK of force exerted (where 1=greatest force and 4 = least force

¼ full

½ full

¾ full

full

““We Do” - ANSWERS: We Do” - ANSWERS:

1. What acceleration will result when a 12 N net force applied to a 3 kg object? 1. What acceleration will result when a 12 N net force applied to a 3 kg object? a = F/m ; a = a = F/m ; a = 12 kg m/s/s12 kg m/s/s = 4 m/s/s = 4 m/s/s

3 kg3 kg

  2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s22. . Determine the mass.Determine the mass.

m = F/a ; m = m = F/a ; m = 16 kg m/s/s16 kg m/s/s = 3.2 kg = 3.2 kg 5 m/s/s5 m/s/s 3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec?3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec? F = ma ; F =F = ma ; F = ( (66 kg)1m/sec/sec or 66 N66 kg)1m/sec/sec or 66 N

4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec?4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec? F = ma ; F =F = ma ; F = 10001000 kg x 9.8 m/sec/sec = 9800 N kg x 9.8 m/sec/sec = 9800 N

5. What is the acceleration of a 1400 kg car when a force of 2800 N is applied.5. What is the acceleration of a 1400 kg car when a force of 2800 N is applied. a = F/m ; a = a = F/m ; a = 2800 kg m/s/s2800 kg m/s/s = 2 m/s/s = 2 m/s/s 1400 kg1400 kg