A person pushes a 16.0-kg shopping cart at a constant velocity for a distance of 26.0 m. She pushes in a direction 22.0° below the horizontal. A 38.0-N frictional force opposes the motion of the cart.
So much for the facts. What is the question?
To find the force applied by the person, we need to analyze the forces acting on the shopping cart.
First, let's break down the forces into their horizontal and vertical components:
- The force applied by the person has a horizontal component and a vertical component.
- The frictional force opposes the motion, so it has a horizontal component equal in magnitude but opposite in direction to the horizontal component of the force applied by the person.
Next, let's calculate the horizontal and vertical components of the force applied by the person:
- The horizontal component can be found by multiplying the magnitude of the force applied by the cosine of the angle below the horizontal: F_horizontal = F_applied * cos(angle).
- The vertical component can be found by multiplying the magnitude of the force applied by the sine of the angle below the horizontal: F_vertical = F_applied * sin(angle).
Since the cart is moving at a constant velocity, the net force acting on the cart must be zero. The net force is the vector sum of all forces acting on the cart.
Now, let's analyze the forces acting on the cart along the horizontal direction:
- The horizontal component of the applied force pushes the cart in the positive horizontal direction.
- The horizontal component of the frictional force opposes the motion, pushing the cart in the negative horizontal direction.
So, the equation for forces along the horizontal direction is:
F_applied * cos(angle) - Frictional force = 0
Now, let's substitute the given values into the equation:
F_applied * cos(22°) - 38 N = 0
From here, we can isolate F_applied:
F_applied * cos(22°) = 38 N
F_applied = 38 N / cos(22°)
By calculating the right side of the equation, we can find the force applied by the person.
However, you have not provided the coefficient of friction or any other information about the frictional force. Without this information, we cannot fully determine the force applied by the person.