The man push with a force of 200 N. The child and sled
combo have a mass of 30 kg and the coefficient of kinetic friction is
0.15.The angle between the slides and the ground is 30 degrees.
What is the frictional force opposing his efforts?
What is the acceleration of the child?
To find the frictional force opposing his efforts, we can use the formula:
frictional force = coefficient of kinetic friction * normal force
The normal force is the force pushing up on the sled and child combo from the ground, which is equal in magnitude to the weight of the sled and child combo:
normal force = mass * gravitational acceleration * cos(theta)
where theta is the angle between the sled and the ground. Plugging in the given values, we get:
normal force = 30 kg * 9.8 m/s^2 * cos(30 degrees) = 255 N
Now, we can plug this value and the given coefficient of kinetic friction into the formula for frictional force:
frictional force = 0.15 * 255 N = 38.25 N
Therefore, the frictional force opposing his efforts is 38.25 N.
To find the acceleration of the child, we can use Newton's second law:
force = mass * acceleration
The force acting on the sled and child combo is the force the man is pushing with, minus the frictional force opposing his efforts:
force = 200 N - 38.25 N = 161.75 N
Plugging in the given mass, we get:
161.75 N = 30 kg * acceleration
Solving for acceleration, we get:
acceleration = 5.39 m/s^2
Therefore, the acceleration of the child and sled combo is 5.39 m/s^2.
Describe bone marking include refe
Bone markings are features found on bones that serve as attachment sites for muscles, ligaments, and tendons or provide passageways for blood vessels and nerves.
There are two types of bone markings:
1. Projections: protrusions or raised areas on bones that provide attachment sites for muscles and ligaments. Examples include tubercles, trochanters, and processes.
2. Depressions: indentations or grooves on bones that provide passageways for blood vessels and nerves or allow for articulation with other bones. Examples include fossae, sinuses, and foramina.
Some common bone markings include:
1. Tubercle: A small rounded projection or bump on a bone, often used as an attachment site for a tendon or ligament. Examples include the greater and lesser tubercles of the humerus and the tubercle of the ilium.
2. Trochanter: A large, rough projection found only on the femur. It serves as a site for muscle attachment.
3. Process: A bony projection found on various bones. Examples include the transverse process of the vertebrae and the mastoid process of the temporal bone.
4. Fossa: A shallow depression or hollow area on a bone. Examples include the olecranon fossa on the humerus and the subscapular fossa on the scapula.
5. Foramen: An opening or perforation in a bone through which blood vessels or nerves may pass. Examples include the foramen magnum in the skull and the obturator foramen in the hip bone.
To determine the frictional force opposing the man's efforts, we need to calculate the normal force and then use it to calculate the frictional force.
1. Calculate the normal force:
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the child and sled combo. The weight can be calculated using the formula: weight = mass * gravity, where gravity is approximately 9.8 m/s^2.
Weight = 30 kg * 9.8 m/s^2 = 294 N
2. Calculate the frictional force:
The frictional force can be calculated using the formula: frictional force = coefficient of kinetic friction * normal force.
Frictional force = 0.15 * 294 N = 44.1 N
Therefore, the frictional force opposing his efforts is 44.1 N.
To determine the acceleration of the child, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
3. Calculate the net force:
The net force is the force pushing the child and sled combo forward, considering that the force opposing his efforts is the frictional force.
Net force = applied force - frictional force
Net force = 200 N - 44.1 N = 155.9 N
4. Calculate the acceleration:
Acceleration = net force / mass
Acceleration = 155.9 N / 30 kg
Therefore, the acceleration of the child is approximately 5.2 m/s^2.