The man pushes/pulls with a force of 200N. The child and the slide combo has a mass of 30 kg and coefficient of friction is 0.15. The angle between the slide and the ground is 30 degrees. Find the acceleration of the child and what is the frictional forces opposing his efforts
Well, let's slide right into this problem! To calculate the acceleration of the child, we'll need to take into account the force applied by the man, the force of friction, and the weight of the child and the slide combo.
First, let's find the force of friction opposing the motion. The formula for frictional force is given by: force of friction = coefficient of friction × normal force.
The normal force can be calculated by taking the weight of the child and the slide combo and multiplying it by the cosine of the angle between the slide and the ground. So, normal force = mass × gravitational acceleration × cos(angle).
Using the given values, the weight of the child and the slide combo is: weight = mass × gravitational acceleration = 30 kg × 9.8 m/s².
The normal force is then: normal force = 30 kg × 9.8 m/s² × cos(30°).
Now, let's get the force of friction: force of friction = 0.15 × normal force.
To find the net force, we subtract the force of friction from the force applied by the man: net force = force applied by the man - force of friction.
Finally, we can calculate the acceleration using Newton's second law: acceleration = net force / mass.
And there you have it! The acceleration of the child and the frictional force opposing his efforts. Just remember, even when things get slippery, laughter is always the best acceleration!
To find the acceleration of the child, we need to calculate the net force acting on the child-slide combo.
Step 1: Decompose the force applied into components
The force applied by the man can be decomposed into two components: one parallel to the incline (F_parallel) and one perpendicular to the incline (F_perpendicular).
F_parallel = F_applied * sin(theta)
F_parallel = 200N * sin(30°)
F_parallel = 100N
F_perpendicular = F_applied * cos(theta)
F_perpendicular = 200N * cos(30°)
F_perpendicular = 173.21N
Step 2: Calculate the gravitational force
The gravitational force acting on the child-slide combo can be calculated using the formula: F_gravity = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = 30kg * 9.8 m/s^2
F_gravity = 294N
Step 3: Calculate the normal force
The normal force (N) acting on the child is equal to the perpendicular component of the gravitational force, as the child is on an incline.
N = F_perpendicular
N = 173.21N
Step 4: Calculate the frictional force
The frictional force can be calculated using the formula: F_friction = u * N, where u is the coefficient of friction.
F_friction = 0.15 * N
F_friction = 0.15 * 173.21N
F_friction = 25.98N
Step 5: Calculate the net force
The net force (F_net) acting on the child-slide combo is equal to the difference between the force parallel to the incline and the frictional force opposing it.
F_net = F_parallel - F_friction
F_net = 100N - 25.98N
F_net = 74.02N
Step 6: Calculate the acceleration
The acceleration (a) of the child-slide combo can be calculated using Newton's second law: F_net = m * a, where m is the mass.
74.02N = 30kg * a
a = 74.02N / 30kg
a = 2.47 m/s^2
Therefore, the acceleration of the child-slide combo is 2.47 m/s^2.
The frictional force opposing the child's efforts is equal to 25.98N.
To find the acceleration of the child and the frictional force opposing his efforts, we can break down the forces acting on the system.
First, let's resolve the force applied by the man into its vertical and horizontal components.
Vertical component: The vertical component of the force applied by the man does not affect the sliding motion of the child, as it is perpendicular to the direction of motion. Therefore, it does not contribute to the acceleration or friction.
Horizontal component: The horizontal component of the force applied by the man is responsible for the acceleration of the child and the frictional force opposing his efforts.
To calculate the horizontal component of the force, we use trigonometry. The horizontal component can be calculated as follows:
Force_horizontal = Force_applied * cos(angle),
where Force_applied = 200N and angle = 30 degrees.
Substituting the values, we get:
Force_horizontal = 200N * cos(30 degrees)
Force_horizontal = 200N * √3/2
Force_horizontal ≈ 173.2N
Now let's calculate the acceleration of the child using Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
Net force = Force_horizontal - Frictional force
Frictional force = coefficient of friction * normal force
The normal force is the force acting perpendicular to the slide. In this case, it is equal to the weight of the child and the slide combo, which is given by the equation:
Normal force = Mass * gravity,
where Mass = 30kg and gravity = 9.8 m/s^2.
Normal force = 30kg * 9.8 m/s^2
Normal force = 294N
Now we can calculate the frictional force:
Frictional force = 0.15 * 294N
Frictional force ≈ 44.1N
Net force = Force_horizontal - Frictional force
Net force = 173.2N - 44.1N
Net force ≈ 129.1N
Using Newton's second law, we can now calculate the acceleration of the child:
Acceleration = Net force / Mass
Acceleration = 129.1N / 30kg
Acceleration ≈ 4.3 m/s^2
Therefore, the acceleration of the child is approximately 4.3 m/s^2 and the frictional force opposing his efforts is approximately 44.1N.
M*g = 30 * 9.8 = 294 N.
Fp = 294*sin30 = 147 N. = Force parallel with slide.
Fn = 294*cos30 = 254.6 N. = Force perpendicular to the ride = Normal.
Fk = u*Fn = 0.15 * 254.6 = 38.2 N. = Force of kinetic friction.
Fap = 200 N. = Force applied.
Fap-Fp-Fk = M*a.
200-147-38.2 = 30*a,
30a = 14.8, a = 0.493 m/s^2.