A 107.0 N grocery cart is pushed 14.0 m along an aisle by a shopper who exerts a constant horizontal force of 40.0 N. If all frictional forces are neglected and the cart starts from rest, what is the grocery cart's final speed?
Duplicate post. Use conservationn of energy. The mass of the cart is
M = W/g = 107/9.8 kg
I showed you the formula to use in your other post of the same question
To find the grocery cart's final speed, we can use the equation of motion:
Final velocity^2 = Initial velocity^2 + 2 * acceleration * distance
In this case, the cart starts from rest, so the initial velocity is 0 m/s. The acceleration can be calculated using Newton's second law of motion:
Force = mass * acceleration
Since all frictional forces are neglected, the only force acting on the cart is the applied force by the shopper, which is 40.0 N. The mass of the grocery cart can be calculated using Newton's second law of motion:
Force = mass * acceleration
Rearranging the equation, we get:
acceleration = Force / mass
Substituting the given values:
acceleration = 40.0 N / 107.0 kg
Next, we need to determine the mass of the grocery cart. We can do so using the equation:
weight = mass * gravity
Given that the weight of the grocery cart is 107.0 N, and the acceleration due to gravity is approximately 9.8 m/s^2, we can rearrange the equation to solve for mass:
mass = weight / gravity
Substituting the given values:
mass = 107.0 N / 9.8 m/s^2
Now that we have found the mass, we can calculate the acceleration:
acceleration = 40.0 N / (107.0 N / 9.8 m/s^2)
With the mass and acceleration determined, we can now calculate the final velocity using the equation of motion:
Final velocity^2 = 0^2 + 2 * acceleration * distance
Substituting the values for acceleration and distance:
Final velocity^2 = 2 * acceleration * 14.0 m
Simplifying:
Final velocity^2 = 2 * (40.0 N / (107.0 N / 9.8 m/s^2)) * 14.0 m
Finally, we can solve for the final velocity by taking the square root of both sides:
Final velocity = sqrt(2 * (40.0 N / (107.0 N / 9.8 m/s^2)) * 14.0 m)
Calculating this equation will give us the final speed of the grocery cart.