A shopper in a supermarket pushes a loaded 32 kg cart with a horizontal force of 12 N. How far will the cart move in 3.5 s if the shopper places an 85 N child in the cart before pushing?
I don't know how I can add the 85 N to the 32 kg or if I can or how that works in an equation. Yikes.
The mass of the child is Weight/g = 8.7 kg. Add that to the mass of the cart to get Mtotal = 40.7 kg
The acceleration rate of the cart is
a = Force/Mtotal = 12/40.7 = 0.29 m/s^2
For the distance X moved in t = 3.5 s, use the equation
X = (1/2) a t^2
which assumes an iniital speed of zero.
I'm sorry 541 people left you on read.
Well, it seems like we have quite the heavy load to calculate here! Don't worry, I'm here to help with a sprinkle of humor.
To start, let's take care of the extra weight. Adding an 85 N child to the 32 kg cart might make it feel like you're pushing a small elephant around! But fear not, we can handle this.
The total mass, or Mtotal, is determined by adding the mass of the cart and the child together. So, we have Mtotal = 32 kg + 8.7 kg of pure child cuteness, giving us 40.7 kg of shopping adventure.
Now, let's tackle the acceleration rate of the cart. Remember, acceleration is equal to the force divided by the mass. So, a = 12 N / 40.7 kg ≈ 0.29 m/s^2.
Finally, to find the distance the cart moves in 3.5 seconds, we can use the equation X = (1/2) a t^2. Plugging in our values, we get X = (1/2) * 0.29 m/s^2 * (3.5 s)^2.
Calculating that out, we find that the cart will move approximately X = 1.72 meters in 3.5 seconds. That's quite a distance to travel, especially with a little passenger aboard!
So, there you have it! Don't forget to bring some extra clown noses and balloons for your shopping adventure. Happy pushing!
To find the distance the cart moves in 3.5 seconds, we can use the equation X = (1/2) a t^2, where X is the distance, a is the acceleration rate, and t is the time.
First, let's calculate the acceleration rate of the cart:
a = Force/Mtotal = 12 N / 40.7 kg = 0.29 m/s^2
Now, plug in the values into the equation:
X = (1/2) * 0.29 m/s^2 * (3.5 s)^2
Calculating this equation:
X = (1/2) * 0.29 m/s^2 * 12.25 s^2
X = 0.145 m/s^2 * 12.25 s^2
X = 1.77875 m
Therefore, the cart will move approximately 1.78 meters in 3.5 seconds after placing the 85 N child in the cart.
To calculate the distance the cart moves, you will need to use the equation X = (1/2) a t^2, where X is the distance, a is the acceleration, and t is the time.
First, you need to calculate the total mass of the cart and the child. Since the mass is given in kilograms, you can directly add the masses together.
The mass of the cart is given as 32 kg. To convert the weight of the child (85 N) to mass, divide it by the acceleration due to gravity, which is approximately 9.8 m/s^2.
Mass of the child = Weight / (acceleration due to gravity) = 85 N / 9.8 m/s^2 ≈ 8.7 kg
The total mass of the cart and the child is the sum of the mass of the cart and the mass of the child.
Total mass (Mtotal) = Mass of the cart + Mass of the child = 32 kg + 8.7 kg = 40.7 kg
Next, calculate the acceleration of the cart using the force applied and the total mass of the system.
acceleration (a) = Force (F) / Total mass (Mtotal) = 12 N / 40.7 kg ≈ 0.29 m/s^2
Now that you have the acceleration, you can use the equation X = (1/2) a t^2 to find the distance X moved in time t.
distance (X) = (1/2) acceleration (a) * time (t)^2 = (1/2) * 0.29 m/s^2 * (3.5 s)^2 ≈ 0.881 meters
Therefore, the cart will move approximately 0.881 meters in 3.5 seconds when the shopper places an 85 N child in the cart before pushing.