Question

You push a shopping cart filled with groceries (total mass = 20 kg) by applying a force to the cart 30° from the horizontal. If the force you apply has a magnitude of 86 N, what is the cart’s acceleration? Assume negligible friction.You push a shopping cart filled with groceries (total mass = 20 kg) by applying a force to the cart 30° from the horizontal. If the force you apply has a magnitude of 86 N, what is the cart’s acceleration? Assume negligible friction.2.2 m/s25.5 m/s23.7 m/s24.3 m/s2

Answer 1

`3.7m/s^(2)`

Step-by-step explanation:

The forces acting on the cart is displayed in the attached file below.

Since the motion is only along the horizontal, we can conclude that the force bringing about that motion is the horizontal force.And from second newton law of motion, we deduce that

F=ma,

F=force, m=mass and a=acceleration

from the given question,

F=86N, mass,m=20kg,

Hence we can write the horizontal component of the force as

`F_(X)=Fcos\alpha \\F_(x)=86cos30\\F_(x)=74.48\\Hence \\a=(F_(x))/(m) \\a=(74.48)/(20)\\ a=3.7m/s^(2)`

Answer 2

3.72 m/s²

Step-by-step explanation:

Horizontal component of the force applied = Fcosθ = 86 cos 30 = 74.478 N

Force = mass × acceleration = 74.478 N

ma = 74.478 N

a = 74.478 / 20 since friction can be neglected = 3.72 m/s²