5. What is the acceleration of a 20 N object that is pulled up a 30° incline by a 25 N force? The coefficient of friction is 0.30
The acceleration will be the NET force (Pull - friction) divided by the mass.
I will be glad to critique your work.
A car travels at a speed of 25 m/s on a flat stretch of road. The driver must
maintain pressure on the accelerator to keep the car moving at this speed.
What is the net work done on the car over a distance of 250 m?
To find the acceleration of the object, we can start by calculating the net force acting on the object.
1. First, we need to determine the force component parallel to the incline. We can calculate this using the formula F_parallel = force * cos(angle). In this case, the force is 25 N and the angle is 30°, so F_parallel = 25 N * cos(30°).
F_parallel = 25 N * cos(30°)
F_parallel = 25 N * √(3)/2
F_parallel ≈ 21.65 N
2. Next, we need to determine the force of friction. The formula for frictional force is F_friction = coefficient of friction * normal force. In this case, the coefficient of friction is 0.30, and the normal force is the component of the weight perpendicular to the incline. The perpendicular component is given by weight * sin(angle). The weight of the object is 20 N, and the angle is 30°.
Normal force = weight * sin(angle)
Normal force = 20 N * sin(30°)
Normal force = 10 N
F_friction = coefficient of friction * normal force
F_friction = 0.30 * 10 N
F_friction = 3 N
3. Now, we can calculate the net force by subtracting the force of friction from the force parallel to the incline.
Net force = F_parallel - F_friction
Net force = 21.65 N - 3 N
Net force = 18.65 N
4. Finally, we can calculate the acceleration of the object using Newton's second law. The formula is acceleration = net force / mass. In this case, we need to convert the weight (which is a force) into mass. Since weight = mass * acceleration due to gravity, we can solve for mass by dividing the weight by the acceleration due to gravity (9.8 m/s²).
Mass = weight / acceleration due to gravity
Mass = 20 N / 9.8 m/s²
Mass ≈ 2.04 kg
Acceleration = net force / mass
Acceleration = 18.65 N / 2.04 kg
Acceleration ≈ 9.14 m/s²
Therefore, the acceleration of the 20 N object being pulled up a 30° incline by a 25 N force, with a coefficient of friction of 0.30, is approximately 9.14 m/s².