Question

newton: force and motion, continued
part 2: newtons second law
isaac newton expressed the relationship between force, mass, and acceleration in his sec-
ond law. this law is so important that it became the basis for much of modern physics.
in fact, newtons contribution to science was so great that the unit for force, the newton
(n), was named after him. a newton is defined as the force needed to produce an accel-
eration of ( 1 mathrm{~m} / mathrm{s}^{2} ) on a ( 1 mathrm{~kg} ) object. therefore, ( 1 mathrm{~n}=1 mathrm{~kg} \times 1 mathrm{~m} / mathrm{s}^{2} ). the equation for
newtons second law is given below.
equation:
force ( =) mass ( \times ) acceleration
( f=m \times a )
if you know two of the values in this equation, you can calculate the third by
changing the equation around, as follows:
acceleration ( =\frac{\text { force }}{\text { mass }} ) and mass ( =\frac{\text { force }}{\text { acceleration }}
sample problem: a soccer ball accelerates at a rate of ( 22 mathrm{~m} / mathrm{s}^{2} ) forward when kicked by
a player. the soccer ball has a mass of ( 0.5 mathrm{~kg} ). how much force was applied to the ball
to produce this acceleration?
force ( =) mass ( \times ) acceleration
force ( =0.5 mathrm{~kg} \times 22 mathrm{~m} / mathrm{s}^{2} )
force ( =11 mathrm{~kg} \times mathrm{m} / mathrm{s}^{2} )
force ( =11 mathrm{~n} )
use the equations above to complete the following problems:

1. calculate the force necessary to accelerate the following vehicles at the rate of acceler-

ation shown in the illustration.
a.
( m = 115 mathrm { kg } )
( a = 6 mathrm { m } / mathrm { s } ^ { 2 } )
force ( =)
b.
( m = 3950 mathrm { kg } )
force ( =)
c.
( m = 14,056 mathrm { kg } )
( a = 112 mathrm { m } / mathrm { s } ^ { 2 } ) west
force ( = )

Explanation:

Step1: Use Newton's second law formula

Newton's second law is \(F = m\times a\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration.

Step2: Calculate force for part a

Given \(m = 115\space kg\) and \(a=6\space m/s^{2}\), substitute into the formula: \(F = 115\times6\).

$$F = 690\space N$$

Step3: Calculate force for part b

Given \(m = 3950\space kg\) and \(a = 25\space m/s^{2}\), substitute into the formula: \(F=3950\times25\).

$$F = 98750\space N$$

Step4: Calculate force for part c

Given \(m = 14056\space kg\) and \(a = 112\space m/s^{2}\), substitute into the formula: \(F = 14056\times112\).

$$F=1574272\space N$$

Answer:

a. \(690\space N\)
b. \(98750\space N\)
c. \(1574272\space N\)