A small car of mass 826 kg isparked behind a small truck of mass 1592 kg on a le

Question

A small car of mass 826 kg isparked behind a small truck of mass 1592 kg on a level road. The brakes of both the car and the truck are off so that they arefree to roll with negligible friction. A 35 kg woman sitting on thetailgate of the truck shoves the car away by exerting a constantforce on the car with her feet. The car accelerates at1.6m/s2.

What is the acceleration of the truck? Answer in units ofm/s2. What is the magnitude of the force exertedon the car? Answer in units of N. A small car of mass 826 kg isparked behind a small truck of mass 1592 kg on a level road. The brakes of both the car and the truck are off so that they arefree to roll with negligible friction. A 35 kg woman sitting on thetailgate of the truck shoves the car away by exerting a constantforce on the car with her feet. The car accelerates at1.6m/s2.

What is the acceleration of the truck? Answer in units ofm/s2. What is the magnitude of the force exertedon the car? Answer in units of N. What is the magnitude of the force exertedon the car? Answer in units of N.

Explanation / Answer

   a.   According to law ofconservation of linear momentum    momentum of truck andwoman   +   momentum ofcar   =   0    ( as initially car and truck were atrest)   (mt   +   mw)* vt   +   mc *vc   =   0    m represent mass and v represent velocity.Subscript t, w and c refer to truck, woman and carrespectively.    =>   (1592 + 35) *vt   +   826 *vc   =   0    But   vt   =   at*t       and      vc   =   ac* t    where a is respective acceleration.    1627 * at *t   =   - 826 * 1.6 * t    acceleration of thetruck   at   =   -1321.6 / 1627                                                 =   -0.812   m/s2    -ve sign is due to the fact that the truckis accelerated in direction opposite to the car.    -ve sign is due to the fact that the truckis accelerated in direction opposite to the car.    b.   Force oncar   Fc   =   mc* ac                                        =   826* 1.6                                        =   1321.6   N                                        =   826* 1.6                                        =   1321.6   N

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