A car is towing a trailer along a horizontal straight road using a horizontal tow-bar. The masses of the car and trailer are 1050kg and 200kg respectively. The resistance to motion of the car is 850N and the resistance to motion of the trailer is 150N.

i) At an instant when driving force exerted by the car is 1100N, find...
a) the acceleration of the car,
b) the pulling force exerted on the trailer.

ii) At another instant the pulling force exerted on the trailer to zero.
a) show that the acceleration of the car is 0.75 ms^-2.
b) find the driving force exerted by the car.

Hashsh

you would resolve using F=ma

so 100=1250a
so a=0.08m/s-2

To solve this problem, we need to apply Newton's second law of motion, F = ma, where F is the net force acting on an object, m is its mass, and a is its acceleration.

i)

a) To find the acceleration of the car, we need to determine the net force acting on it. The net force is the difference between the driving force exerted by the car and the resistance to motion. In this case, the resistance to motion of the car is given as 850N.

Net force on the car = Driving force - Resistance to motion
= 1100N - 850N
= 250N

Now, we can use Newton's second law to find the acceleration of the car. The mass of the car is given as 1050kg.

Acceleration of the car = Net force / Mass
= 250N / 1050kg
= 0.238 m/s² (rounded to 3 decimal places)

b) To find the pulling force exerted on the trailer, we can use the fact that the acceleration of the car is the same as the acceleration of the trailer when they are connected.

Acceleration of the trailer = Acceleration of the car = 0.238 m/s²

Using Newton's second law, we can calculate the pulling force exerted on the trailer. The mass of the trailer is given as 200kg.

Pulling force on the trailer = Mass of the trailer * Acceleration of the trailer
= 200kg * 0.238 m/s²
= 47.6N (rounded to 1 decimal place)

ii)

a) If the pulling force exerted on the trailer is zero, it means the net force acting on the trailer is also zero. This implies that the resistance to motion of the trailer is equal to the driving force exerted by the car. The resistance to motion of the trailer is given as 150N.

Driving force exerted by the car = Resistance to motion of the trailer
= 150N

Now, we know that the acceleration of the car is the same as in part (i). So, the acceleration of the car is 0.238 m/s².

b) To find the driving force exerted by the car, we can use Newton's second law. The mass of the car is given as 1050kg.

Driving force exerted by the car = Mass of the car * Acceleration of the car
= 1050kg * 0.238 m/s²
= 249.9N (rounded to 1 decimal place)

Therefore, the driving force exerted by the car is approximately 249.9N.