Question

An 85 N shopping cart is pushed by a shopper with a horizontal force of 43 N down an aisle 16 m long. If the cart starts at rest, what is the final velocity at the end of the aisle rounded to the nearest thousandth? (Hint: the work-kinetic energy theorem might be helpful here)

Answer 1

Using the work-kinetic energy theorem and assuming no other forces acting on the cart, the final velocity of the shopping cart after being pushed by the shopper is approximately 3.968 m/s.

Step-by-step explanation:

To determine the final velocity of the shopping cart after being pushed down the aisle, we can make use of the work-kinetic energy theorem.

This theorem states that the net work done on an object is equal to its change in kinetic energy.

First, we find the work done by the shopper's force:

Work (W) = Force (F) × Distance (d)

W = 43 N × 16 m

W = 688 J

Assuming there is no friction or other forces doing work, the entire work done goes into changing the kinetic energy of the cart. The change in kinetic energy (KE) can be given as:

ΔKE = Work done

ΔKE = ½ m v2 - ½ m u2, where u is the initial velocity, and v is the final velocity.

Since the cart starts from rest, u = 0 m/s, and thus the equation simplifies to:

½ m v2 = 688 J

v2 = (2 × 688 J) / m

To find m (mass), use the weight (W = mg), where g is the acceleration due to gravity (9.8 m/s2).

m = 85 N / 9.8 m/s2

≈ 8.673 kg

v2 ≈ (2 × 688 J) / 8.673 kg

v ≈ √(1376 J / 8.673 kg)

v ≈ 3.968 m/s

Therefore, rounding to the nearest thousandth, the shopping cart's final velocity is 3.968 m/s.