11.2 The baggage truck A has a mass of 800 kg and is used to pull two cars, each with a mass of 300 kg. If the tractive force F on the truck is F = 480 N, determine the initial acceleration of the truck. What is the acceleration of the truck if the coupling at C suddenly fails? The car wheels are free to roll; neglect the mass of the wheels.
Ans: a = 0.343 m/s2, a = 0.436 m/s2
acceleration= force/total mass
total mass is 2000kg, if my math is correct.
I don't know where C is, but just subtract the mass following C.
To determine the initial acceleration of the truck, we can apply Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
1. Calculate the total mass of the system:
Total mass = mass of truck + mass of cars
Total mass = 800 kg + (2 * 300 kg)
Total mass = 800 kg + 600 kg
Total mass = 1400 kg
2. Calculate the net force acting on the system:
Net force = Tractive force - Frictional force
Net force = 480 N - 0 (assuming no frictional force)
Net force = 480 N
3. Apply Newton's second law to calculate the initial acceleration:
Net force = Total mass * Acceleration
480 N = 1400 kg * Acceleration
Acceleration = 480 N / 1400 kg
Acceleration = 0.343 m/s²
Therefore, the initial acceleration of the truck is 0.343 m/s².
To determine the acceleration of the truck if the coupling at C suddenly fails, we can consider that the cars will roll freely, and the only force acting on the truck will be the tractive force.
1. Calculate the effective mass of the system when the coupling fails:
Effective mass = mass of truck + mass of cars
Effective mass = 800 kg + 300 kg + 300 kg
Effective mass = 800 kg + 600 kg
Effective mass = 1400 kg
2. Apply Newton's second law to calculate the acceleration when the coupling fails:
Net force = Tractive force - Frictional force
Net force = 480 N - 0 (assuming no frictional force)
Net force = 480 N
Net force = Effective mass * Acceleration
480 N = 1400 kg * Acceleration
Acceleration = 480 N / 1400 kg
Acceleration = 0.343 m/s²
Therefore, the acceleration of the truck when the coupling at C suddenly fails is 0.436 m/s².
To determine the initial acceleration of the truck, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
First, let's calculate the total mass of the system. The total mass is the sum of the mass of the truck and the mass of the two cars:
Total mass (M) = Mass of truck (m1) + Mass of car 1 (m2) + Mass of car 2 (m3)
M = m1 + m2 + m3
M = 800 kg + 300 kg + 300 kg
M = 1400 kg
Now, we can calculate the net force acting on the system, which is equal to the tractive force exerted by the truck:
Net force (Fnet) = Tractive force (F)
Fnet = 480 N
Finally, we can calculate the initial acceleration of the truck using Newton's second law:
a = Fnet / M
a = 480 N / 1400 kg
a ≈ 0.343 m/s^2
So, the initial acceleration of the truck is approximately 0.343 m/s^2.
Next, let's determine the acceleration of the truck if the coupling at C suddenly fails. In this case, the truck would no longer be able to pull the cars, so we need to consider the forces acting on the truck.
When the coupling fails, the truck experiences a friction force due to the car wheels rolling freely. This friction force opposes the motion of the truck and hence acts in the opposite direction of the original tractive force.
Now, let's calculate the net force acting on the truck when the coupling fails.
Net force (Fnet) = Tractive force (F) - Friction force (Ff)
Fnet = F - Ff
The friction force (Ff) can be calculated using the coefficient of rolling resistance (μ) and the normal force (N) exerted on the truck by the rolling cars:
Ff = μ * N
Since the truck is pulling two cars, the normal force exerted on the truck is equal to the weight of the cars:
N = (m2 + m3) * g
N = (300 kg + 300 kg) * 9.8 m/s^2
N ≈ 5880 N
Now, we can calculate the friction force:
Ff = μ * N
Ff = μ * 5880 N
The coefficient of rolling resistance (μ) varies depending on the surface condition and the type of tires. For the purpose of this explanation, let's assume μ = 0.1.
Ff = 0.1 * 5880 N
Ff ≈ 588 N
Now, we can calculate the net force acting on the truck:
Fnet = F - Ff
Fnet = 480 N - 588 N
Fnet ≈ -108 N (negative because the net force acts in the opposite direction of the tractive force)
Finally, we can calculate the acceleration of the truck when the coupling fails:
a = Fnet / M
a = -108 N / 1400 kg
a ≈ -0.436 m/s^2
So, the acceleration of the truck when the coupling fails is approximately -0.436 m/s^2.