How much force is needed to bring a 3200 lb car from rest to a velocity of 44 ft/s in 8 seconds? Please indicate the formula used.
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The formula to use is
F = M * a
M must be in slugs (and equals 99.4 slugs) and the acceleration is
a = (44 ft/s)/8 s = 5.5 ft/s^2.
The force F that you compute,
99.4 slugs * 5.4 ft/s^2, will be in pounds.
Note that 1 lb force = 1 slug*ft/s^2
Although 1 pound of mass has a weight force of 1 pound on Earth, it is essential that Weight and mass have different units when doing physics and engineering problems, because force and mass are NOT the same thing.
Ok sir! TNX!
Well, the force required to accelerate an object can be calculated using Newton's second law of motion: force equals mass times acceleration (F = ma). In this case, we need to find the force required to accelerate the car from rest to a velocity of 44 ft/s in 8 seconds.
First, let's convert the mass of the car from pounds to slugs (a unit used to measure mass in the imperial system). Since 1 slug is equal to 32.174 pounds, we divide 3200 pounds by 32.174 to get approximately 99.515 slugs.
Next, we'll calculate the acceleration using the formula acceleration equals change in velocity divided by time (a = Δv / t). The change in velocity is 44 ft/s (final velocity) - 0 ft/s (initial velocity), which equals 44 ft/s. Dividing this by the time of 8 seconds, we get an acceleration of 5.5 ft/s².
Now that we have the mass and acceleration, we can calculate the force using Newton's second law. F = ma, so the force required to accelerate the car is approximately 547.33 pounds-force.
Please note that this is a simplified calculation, and there are other factors that could affect the force required, such as friction and air resistance. So, this is just an estimate for a simplistic scenario.
To determine the force required to accelerate a car, we can use Newton's second law of motion:
Force (F) = mass (m) × acceleration (a)
First, let's convert the car's weight from pounds (lb) to mass in slugs (since the acceleration will be given in ft/s²):
Given:
Weight of car (W) = 3200 lb
Acceleration of car (a) = (final velocity - initial velocity) / time = (44 ft/s - 0 ft/s) / 8 s
To convert the weight to mass, we'll use the gravitational constant (g) of 32.17 ft/s²:
m = W / g
Substituting the given values:
m = 3200 lb / 32.17 ft/s²
Next, we can calculate the acceleration:
a = (44 ft/s - 0 ft/s) / 8 s
Finally, we can substitute the values of mass and acceleration into the formula to find the force:
F = m × a
Let's substitute the values and solve the formula step by step:
m = 3200 lb / 32.17 ft/s²
m ≈ 99.60 slugs
a = (44 ft/s - 0 ft/s) / 8 s
a ≈ 5.50 ft/s²
F = 99.60 slugs × 5.50 ft/s²
F ≈ 547.80 lb·ft/s²
Therefore, approximately 548 lb·ft/s² of force is needed to bring the 3200 lb car from rest to a velocity of 44 ft/s in 8 seconds.
To calculate the force required to bring a car from rest to a certain velocity, you can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the acceleration can be calculated using the formula:
a = (final velocity - initial velocity) / time
Let's break down the formula and calculate the force step-by-step:
1. Convert the car's weight from pounds to slugs:
1 slug = 32.174 pounds
Weight of the car = 3200 lb / 32.174 lb/slug ≈ 99.53 slugs
2. Convert the velocity from ft/s to ft/s^2:
a = (44 ft/s - 0 ft/s) / 8 s ≈ 5.5 ft/s^2
3. Calculate the force (F) using Newton's second law of motion:
F = m * a ≈ 99.53 slugs * 5.5 ft/s^2
Therefore, the force required to bring the car from rest to a velocity of 44 ft/s in 8 seconds is approximately 547.41 lb.
Please note that this calculation assumes linear acceleration throughout the motion and neglects factors such as friction and air resistance, which may affect the actual force required.