A 22.7 kg mass attached to a spring scale rests

on a smooth, horizontal surface. The spring
scale, attached to the front end of a boxcar,
reads T = 21.9 N when the car is in motion.
If the spring scale reads zero when the car
is at rest, determine the acceleration of the
car, when it is in motion.

To determine the acceleration of the car when it is in motion, we can use Newton's second law of motion:

F = ma

where F is the net force acting on the car, m is the mass of the car, and a is the acceleration of the car.

In this case, the only force acting on the car is the tension force measured by the spring scale (T = 21.9 N). Therefore, the net force on the car is equal to the tension force:

F = T

Substituting this into Newton's second law, we get:

T = ma

Now we need to consider the weight force acting on the car, which can be calculated using the equation:

Weight = mass * gravity

where gravity is the acceleration due to gravity (approximately 9.8 m/s^2).

Weight = 22.7 kg * 9.8 m/s^2 = 222.46 N

Since the spring scale reads zero when the car is at rest, we can conclude that the tension force is equal to the weight force when the car is not in motion:

T = Weight

Therefore:

T = ma
222.46 N = 22.7 kg * a

Solving for a, we find:

a = 222.46 N / 22.7 kg
a ≈ 9.8 m/s^2

So, the acceleration of the car when it is in motion is approximately 9.8 m/s^2.

To determine the acceleration of the car when it is in motion, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = ma).

In this scenario, the force acting on the mass is provided by the tension in the spring scale, which is equal to 21.9 N. The mass of the object is 22.7 kg. Therefore, the equation can be written as:

F = ma

21.9 N = 22.7 kg * a

Solving for acceleration (a):

a = 21.9 N / 22.7 kg

a ≈ 0.964 m/s²

Therefore, the acceleration of the car when it is in motion is approximately 0.964 m/s².