100k views
1 vote
A force F, with a magnitude of 17.60 N, acts on an object with a mass of m = 1.25 kg parallel to the plane of the incline as shown in the figure. The angle of the incline is θ θ = 43.4°. The object is observed to move at a constant velocity of 3.81 m/s up on the incline. Calculate the magnitude of the frictional force acting on the object.

User Sanga
by
8.9k points

1 Answer

3 votes

Answer:

17.60 N

Explanation:

To calculate the magnitude of the frictional force acting on the object, we can use the following steps:

Calculate the gravitational force acting on the object.

Determine the component of the gravitational force parallel to the incline.

Calculate the net force acting on the object up the incline.

Calculate the frictional force.

Let's break it down step by step:

Calculate the gravitational force acting on the object:

The gravitational force can be calculated using the formula:

F_gravity = m * g

Where:

F_gravity is the gravitational force.

m is the mass of the object (1.25 kg).

g is the acceleration due to gravity (approximately 9.81 m/s²).

F_gravity = 1.25 kg * 9.81 m/s² = 12.2625 N

Determine the component of the gravitational force parallel to the incline:

The component of the gravitational force acting parallel to the incline can be calculated using trigonometry. This component is given by:

F_parallel = F_gravity * sin(θ)

Where:

F_parallel is the component of the gravitational force parallel to the incline.

θ is the angle of the incline (43.4°).

F_parallel = 12.2625 N * sin(43.4°) ≈ 8.668 N

Calculate the net force acting on the object up the incline:

Since the object is moving at a constant velocity, the net force acting on it must be zero. Therefore, the net force is equal to the force applied minus the frictional force:

Net Force = F_applied - Frictional Force

We know the applied force (F_applied) is 17.60 N, and the object is moving up the incline, so the net force is in the same direction as the applied force:

Net Force = 17.60 N - Frictional Force

Since the object is moving at a constant velocity, Net Force = 0:

0 = 17.60 N - Frictional Force

Calculate the frictional force:

Now, solve for the frictional force:

Frictional Force = 17.60 N

So, the magnitude of the frictional force acting on the object is 17.60 N.

User Mor Paz
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories