A 102.0 N grocery cart is pushed 13.0 m by a shopper who exerts a constant horizontal force of 54.0 N. If all frictional forces are neglected and the cart starts from rest, what is its final speed?
54*13=1/2 mv^2 solve for v
To find the final speed of the grocery cart, we can apply 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.
First, let's calculate the acceleration of the cart using Newton's second law:
F_net = m * a
Here, F_net is the net force, m is the mass of the cart, and a is the acceleration of the cart. Since the net force is the force applied by the shopper pushing the cart, we can substitute F_net with the force applied:
54.0 N = m * a
To find the mass of the cart, we need to use the formula:
Weight = mass * gravitational acceleration
Given that the weight of the cart is 102.0 N, and the gravitational acceleration is approximately 9.8 m/s^2, we can rearrange the formula to solve for mass:
mass = weight / gravitational acceleration
mass = 102.0 N / 9.8 m/s^2
Now, substitute the calculated mass value into the equation for acceleration:
54.0 N = (102.0 N / 9.8 m/s^2) * a
Simplify the expression:
54.0 N = 10.408 N * a
Now, solve for acceleration (a):
a = 54.0 N / 10.408 N
a ≈ 5.19 m/s^2
Next, we can use the kinematic equation to find the final speed of the cart, knowing the initial velocity (0 m/s), displacement (13.0 m), and acceleration (5.19 m/s^2):
v^2 = v_initial^2 + 2 * a * d
Here, v_initial is the initial velocity, v^2 is the final velocity squared, a is the acceleration, and d is the displacement. Rearrange the equation to solve for v:
v^2 = 0 + 2 * 5.19 m/s^2 * 13.0 m
v^2 = 134.94 m^2/s^2
To find the final velocity (v), take the square root of both sides:
v ≈ √134.94 m^2/s^2
v ≈ 11.6 m/s
Therefore, the final speed of the grocery cart is approximately 11.6 m/s.