A shopper exerts a force on a cart of 64N at an angle of 30° below the horizontal.
a.) How much force pushes the cart in a forward direction?
b.) How much force pushes the cart against the floor?
a. 64cos30
b. 64sin30
To find the force that pushes the cart in a forward direction (horizontal component) and the force that pushes the cart against the floor (vertical component), we need to use the concept of vector resolution.
First, let's calculate the horizontal component (force in the forward direction):
a.) To find the force pushing the cart in a forward direction, we need to find the horizontal component of the force exerted by the shopper.
The horizontal component is given by the equation: F_horizontal = F * cosθ
Where:
F is the magnitude of the force exerted by the shopper (64N in this case)
θ is the angle between the force and the horizontal direction (30° below the horizontal)
Substituting the values into the equation, we get:
F_horizontal = 64N * cos(30°)
To find the value, we can evaluate it using a calculator:
F_horizontal ≈ 55.43 N
Therefore, approximately 55.43 N of force pushes the cart in a forward direction.
Now, let's calculate the vertical component (force against the floor):
b.) To find the force pushing the cart against the floor, we need to find the vertical component of the force exerted by the shopper.
The vertical component is given by the equation: F_vertical = F * sinθ
Using the values given:
F_vertical = 64N * sin(30°)
Calculating the value:
F_vertical ≈ 32 N
Approximately 32 N of force pushes the cart against the floor.
Therefore, the answers are:
a.) Approximately 55.43 N of force pushes the cart in a forward direction.
b.) Approximately 32 N of force pushes the cart against the floor.