Question

A 960 kg car is pulling a 310 kg trailer. Together the car and trailer move forward with an acceleration of 2.00 m/s2. Ignore any frictional force of air drag on the car and all frictional forces on the trailer.

(a) Determine the net force on the car.
magnitude

N
direction


(b) Determine the net force on the trailer.
magnitude

N
direction


(c) Determine the force exerted by the trailer on the car.
magnitude

N
direction


(d) Determine the resultant force exerted by the car on the road. (Assume that the forward direction is along the +x-direction.)
magnitude

Answer 1

a)
`F_c=1920\,N`

b)
`F_c=620\,N`

c)
`T=620\,N`

d)
`F_R=9497.39\,N`

`\theta=81.133^(\circ)` from the horizontal.

Step-by-step explanation:

Given:

mass of the car,
`m_c=960\,kg`

mass of trailer,
`m_t=310\,kg`

acceleration of the system,
`a=2\,m.s^(-2)`

(a)

Net force on the car will be in the direction of acceleration given by:

`F_c=m_c.a`

`F_c=960* 2`

`F_c=1920\,N`

(b)

`F_t=m_t.a`

`F_t=310* 2`

`F_t=620\,N`

(c)

Since the car and the trolley are linked together, the link will face a tension force and this will be exerted on the car by the Newton's third law of motion which can be given as:

`T=2* 310`

`T=620\,N`

(d)

Net vertical force acting on the road due to car:

`F_v=m_c.g`

`F_v=960* 9.8`

`F_v=9408\,N`

Net vertical force acting on the road:

`F_h=(960-310)* 2`

`F_h=1300\,N`

Now, the net resultant force:

`F_R=√((1300)^2+(9408)^2)`

`F_R=9497.39\,N`

Angle f the force from horizontal:

`tan\theta=(9408)/(1300)`

`\theta=81.133^(\circ)` from the horizontal.

Answer 2

(a) 2540 N

(b) 620 N

Step-by-step explanation:

mass of car, M = 960 kg

mass of trailer, m = 310 kg

acceleration, a = 2 m/s^2

Let the net force on the car is F and the net force on the trailer is T.

(a) According to the free body diagram, use Newton's second law

F - T = Ma .... (1)

T = ma .... (2)

Adding both the equations

F = (M+m)a

F = (960 + 310) x 2

F = 2540 N

Thus, the force on the car is 2540 N.

(b) By the equation (2), we get

T = 310 x 2 = 620 N

Thus, the force on trailer is 620 N.