A 25.7 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 = 47.6 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 as indicated above.
Answer in units of m/s2

F=ma

47.6 N=25.7 x a
a=47.6/25.7
a=1.85 m/s^2

To determine the acceleration of the car, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, this can be expressed as:

F_net = m * a

In this case, the net force acting on the mass is the tension T indicated by the spring scale. Therefore,

T = F_net

Substituting the given values:

T = 47.6 N

Now, we know that the net force acting on the mass is equal to the force required to accelerate the car. So,

F_net = F = m * a

where F is the force required to accelerate the car, m is the mass of the object attached to the spring scale, and a is the acceleration of the car.

Substituting the given mass:

m = 25.7 kg

We can rearrange the equation to solve for the acceleration:

a = F / m

Substituting the values into the equation:

a = 47.6 N / 25.7 kg

Calculating the division:

a ≈ 1.85 m/s²

Therefore, the acceleration of the car, when it is in motion as indicated above, is approximately 1.85 m/s².

To determine the acceleration of the car, we need to analyze the forces acting on the mass attached to the spring scale.

When the car is in motion, there are two forces acting on the mass:
1. The force due to gravity, which is the weight of the mass (mg)
2. The force measured by the spring scale (T)

Since the spring scale reads zero when the car is at rest, it means there is no net force acting on the mass in the vertical direction. Therefore, the force due to gravity is balanced by the spring scale reading when the car is at rest.

So, we can write the equation for the forces when the car is in motion:

F_net = T - mg

Where:
F_net is the net force acting on the mass
T is the reading of the spring scale (47.6 N)
m is the mass (25.7 kg)
g is the acceleration due to gravity (9.8 m/s^2)

Now, to find the acceleration of the car, we can use Newton's second law of motion:

F_net = m * a

Where:
a is the acceleration of the car.

Setting the net force equal to the product of mass and acceleration, we have:

T - mg = m * a

Substituting the given values, we get:

47.6 N - (25.7 kg * 9.8 m/s^2) = 25.7 kg * a

Simplifying the equation:

47.6 N - 251.86 N = 25.7 kg * a

-204.26 N = 25.7 kg * a

Now, we can solve for the acceleration (a):

a = -204.26 N / 25.7 kg

a ≈ -7.97 m/s^2

Therefore, the acceleration of the car, when it is in motion as indicated, is approximately -7.97 m/s^2.