A constant force is applied to an object, causing the object toaccelerate at 7.4

Question

A constant force is applied to an object, causing the object toaccelerate at 7.4 m/s2. What would the acceleration be if each ofthe following things happened (from the initial state)? (a) the force is doubled ____ m/s2 (b) the object's mass is doubled? ____ m/s2 (c) the force and the object's mass are both doubled ____ m/s2 (d) the force is doubled and the object's mass is halved ____ m/s2

(a) the force is doubled ____ m/s2 (b) the object's mass is doubled? ____ m/s2 (c) the force and the object's mass are both doubled ____ m/s2 (d) the force is doubled and the object's mass is halved ____ m/s2

Explanation / Answer

Let F be the force applied to the object     acceleration a = 7.4 m/s2          we knowthat     F =   m a                                   a =F /m              a) if force is doubled   F =2F                                        a = 2F /m                                      a /2 = F /m                             acceleration a = 7.4 /2    = 3.4m/s2             b) if the objects mass is doubled   that is m= 2m                                      a = F / 2m                                      2a = F /m                             acceleration a = 2 x7.4 = 14.8m/s2           c) ifthe force and the object's mass are both doubled                                acceleration = 2F/2m = a = 7.4 m/s2            d)the force is doubled and the object's mass is halved                              F =2F     ; m = m/2                         a   = F /m                             =   2F/(m/2)   = 4(F/m)                      a/4= F /m                 acceleration a = 7.4 /4 = 1.85m/s2            d)the force is doubled and the object's mass is halved                              F =2F     ; m = m/2                         a   = F /m                             =   2F/(m/2)   = 4(F/m)                      a/4= F /m                 acceleration a = 7.4 /4 = 1.85m/s2

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