A dynamics cart is pulled from rest by a net force of 1.2 N [forward]. The cart moves 6.6 m, reaching a velocity of 3.2 m/ s [forward]. Determine the mass of the cart
To determine the mass of the cart, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
The net force applied to the cart is given as 1.2 N, and the distance it moves is given as 6.6 m. The velocity it reaches is 3.2 m/s.
Using the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (0 m/s in this case), a is the acceleration, and s is the distance traveled, we can find the acceleration of the cart.
3.2^2 = 0 + 2(a)(6.6)
10.24 = 13.2a
a = 10.24 / 13.2
a ≈ 0.775 m/s^2
Now we can use Newton's second law to find the mass of the cart.
F = ma
1.2 = m(0.775)
m = 1.2 / 0.775
m ≈ 1.55 kg
Therefore, the mass of the cart is approximately 1.55 kg.
To determine the mass of the cart, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it, and inversely proportional to its mass. The equation is given as:
F = m * a
Where:
F is the net force applied to the object,
m is the mass of the object, and
a is the acceleration of the object.
In this scenario, the cart is pulled from rest to reach a velocity of 3.2 m/s. The net force acting on it is 1.2 N.
We can calculate the acceleration of the cart using the formula:
a = v / t
Where:
v is the final velocity of the cart, and
t is the time taken for the cart to reach that velocity.
Given that the cart moves 6.6 m and reaches a velocity of 3.2 m/s, we can rearrange the formula to solve for time:
t = d / v
Substituting the given values:
t = 6.6 m / 3.2 m/s
t ≈ 2.0625 seconds
Now we can calculate the acceleration by substituting the values into the formula:
a = 3.2 m/s / 2.0625 s
a ≈ 1.553 m/s^2
Finally, we can determine the mass of the cart by rearranging the formula:
m = F / a
Substituting the given values:
m = 1.2 N / 1.553 m/s^2
m ≈ 0.7728 kg
Therefore, the mass of the cart is approximately 0.7728 kg.
To determine the mass of the cart, 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.
In this case, we know the net force acting on the cart is 1.2 N [forward] and the distance it traveled is 6.6 m. We also know the final velocity is 3.2 m/s [forward].
First, let's find the acceleration of the cart using the equation:
v^2 = u^2 + 2as,
where v is the final velocity, u is the initial velocity (which is 0 m/s since the cart starts from rest), a is the acceleration, and s is the distance.
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s).
Substituting the given values, we get:
a = (3.2^2 - 0^2) / (2 * 6.6).
Simplifying, we find:
a = 1.536 m/s^2 [forward].
Now, we can use Newton's second law to find the mass of the cart. The formula is:
F = ma,
where F is the net force, m is the mass, and a is the acceleration.
Substituting the values, we get:
1.2 N = m * 1.536 m/s^2.
Now, solving for m, we divide both sides of the equation by 1.536:
m = 1.2 N / 1.536 m/s^2.
Calculating, we find:
m ≈ 0.781 kg.
Therefore, the mass of the cart is approximately 0.781 kg.