dETERMINE THE HORIZONTAL FORCE needed to accelerate a 50kg grocery cart from rest to 0.90 m/s in 2.8s if the coefficient of friction between the cart and the floor is 0.20 ?

m*g = 50kg * 9.8N/kg = 490 N. = Wt. of

cart.

Fk = u*mg = 0.2 * 490 = 98 N. = Force of
kinetic friction.

a=(V-Vo)/t = (0.90-0)/2.8 = 0.321 m/s^2/

F-Fk = m*a
F - 98 = 50*0.321 = 16.07
F = 16.07+98 = 114.1 N.

To determine the horizontal force needed to accelerate the grocery 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.

Step 1: Calculate the acceleration of the grocery cart.
Given:
Initial velocity (u) = 0 (since the cart is at rest)
Final velocity (v) = 0.90 m/s
Time taken (t) = 2.8s

Using the equation v = u + at, we can rearrange it to solve for acceleration (a):
a = (v - u) / t

Substituting the given values:
a = (0.90 m/s - 0 m/s) / 2.8s
a = 0.90 m/s / 2.8s
a ≈ 0.321 m/s²

Step 2: Calculate the frictional force acting on the cart.
Given:
Mass (m) = 50 kg
Coefficient of friction (μ) = 0.20

Frictional force (F_f) = μ * m * g, where g is the acceleration due to gravity (approximately 9.8 m/s²).

Substituting the given values:
F_f = 0.20 * 50 kg * 9.8 m/s²
F_f ≈ 98 N

Step 3: Calculate the net force required to accelerate the cart.
Since there is no other force acting in the horizontal direction, the net force is equal to the frictional force.

Net force (F_net) = F_f
F_net ≈ 98 N

Therefore, the horizontal force needed to accelerate the grocery cart is approximately 98 Newtons.

To determine the horizontal force needed to accelerate the grocery cart, we can use Newton's second law, which states that the force acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a). In this case, we want to find the force (F) needed to accelerate the cart from rest to 0.90 m/s in 2.8 seconds.

First, let's calculate the acceleration using the given information:

Acceleration (a) = (final velocity - initial velocity) / time
Acceleration (a) = (0.90 m/s - 0 m/s) / 2.8 s
Acceleration (a) = 0.90 m/s / 2.8 s
Acceleration (a) ≈ 0.3214 m/s²

Next, we need to take into account the frictional force between the cart and the floor. The force of friction can be calculated using the equation:

Force of friction (F_friction) = coefficient of friction (μ) × normal force (N)

Since the cart is on a horizontal surface, the normal force is equal to the weight of the cart, which is given by:

Normal force (N) = mass (m) × gravitational acceleration (g)

The gravitational acceleration (g) is typically approximately 9.8 m/s².

Normal force (N) = 50 kg × 9.8 m/s²
Normal force (N) = 490 N

Now we can calculate the force of friction:

Force of friction (F_friction) = 0.20 × 490 N
Force of friction (F_friction) = 98 N

Finally, we can determine the horizontal force needed to accelerate the grocery cart by adding the force of friction to the force required to accelerate the cart:

Total force (F) = F_friction + F_acceleration
Total force (F) = 98 N + (m × a)
Total force (F) = 98 N + (50 kg × 0.3214 m/s²)
Total force (F) ≈ 98 N + 16.07 N
Total force (F) ≈ 114.07 N

Therefore, the horizontal force needed to accelerate the 50 kg grocery cart from rest to 0.90 m/s in 2.8 seconds, considering the coefficient of friction of 0.20, is approximately 114.07 N.