Pushing a grocery cart with a force of 95N applied at an angle of 35deg own from the horizontal, makes the cart travel at a constant speed of 1.2m/s. What is the frictional force acting on the cart?
well, the pushing force is 95cos35, at constant speed, that is the fricional force.
78N....as suggested above. The horizontal component of the 95 N.
To find the frictional force acting on the cart, we can start by analyzing the force components.
1. Break down the applied force into its horizontal and vertical components.
- The horizontal component of the force can be found using the formula: F_horizontal = F_applied * cos(angle)
- The vertical component of the force can be found using the formula: F_vertical = F_applied * sin(angle)
Given:
F_applied = 95 N (applied force)
angle = 35 degrees
Substituting these values into the formulas, we get:
F_horizontal = 95 * cos(35)
F_vertical = 95 * sin(35)
2. Since the cart is traveling at a constant speed, the net force acting on it is zero. Therefore, the frictional force acting on the cart must oppose the applied force.
3. The frictional force acts horizontally in the opposite direction to the applied force. Therefore, the horizontal component of the frictional force is equal in magnitude but opposite in direction to the horizontal component of the applied force.
F_friction_horizontal = -F_horizontal
4. Since the cart is moving at a constant speed, the frictional force must equal the horizontal component of the applied force.
F_friction_horizontal = F_horizontal = 95 * cos(35)
Therefore, the frictional force acting on the cart is 95 * cos(35).
To find the frictional force acting on the cart, we need to use the equation of motion:
ΣF = m·a
where ΣF is the sum of all forces acting on the cart, m is the mass of the cart, and a is the acceleration of the cart.
In this case, the cart is traveling at a constant speed, which means the net force acting on it is zero. Therefore, the force applied by pushing the cart (95N at an angle of 35 degrees) should be balanced by the frictional force.
First, let's resolve the applied force into horizontal and vertical components. Since the cart is traveling at a constant speed, there is no vertical acceleration, so the vertical component of the applied force does not contribute to the net force. The horizontal component, however, is opposing the frictional force.
The horizontal component of the applied force is calculated as:
F_horizontal = F_applied · cos(angle)
F_horizontal = 95N · cos(35°)
F_horizontal ≈ 78.014N
Since the net force is zero, the frictional force must equal the horizontal component of the applied force:
frictional force = F_horizontal ≈ 78.014N
Therefore, the frictional force acting on the cart is approximately 78.014N.