A 25 kg child is sitting on a 10 kg sled. The child’s older sister is pulling the sled horizontally across the snow at a constant speed of 4 m/s by pulling on a rope with a force of 25 N at an angle of 30o above the horizontal.
[4] a. Draw all appropriate diagrams for the situation.
[3] b. Find the normal force acting on the sled.
[3] c. Find the magnitude of the force of friction between the sled and the snow.
m =35 kg
m g = 35 * 9.81 = 343 Newtons weight
force up from tow line = 25 sin 30 = 12.5 N up
net contact force with snow = 343 - 12.5 = 331 N
speed constant so friction force = horizontal component of friction force
= 25 cos 30 = 21.7 Newtons
TYPO:
speed constant so friction force = horizontal component of tow line force
a. To draw appropriate diagrams for the situation, we need to consider the forces acting on the child and the sled.
1. Free Body Diagram for the Child:
- Draw a vertical line to represent the child.
- Draw an arrow pointing upwards to represent the force of gravity acting on the child, which is equal to the weight of the child (m_child * g).
- Draw another arrow pointing downwards to represent the normal force acting on the child from the sled.
- Draw a horizontal arrow in the direction of motion to represent the pulling force applied by the sister.
2. Free Body Diagram for the Sled:
- Draw a horizontal line to represent the sled.
- Draw an arrow pointing downwards to represent the force of gravity acting on the sled, which is equal to the weight of the sled (m_sled * g).
- Draw an arrow pointing upwards at an angle of 30 degrees to represent the force applied by the sister (tension force).
- Draw a horizontal arrow in the opposite direction of motion to represent the force of friction between the sled and the snow.
b. To find the normal force acting on the sled:
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the weight of the child is supported by the sled.
The normal force on the sled is equal to the weight of the child (m_child * g).
Given that the mass of the child is 25 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the normal force using the formula:
Normal force = m_child * g = 25 kg * 9.8 m/s^2
c. To find the magnitude of the force of friction between the sled and the snow:
The force of friction opposes the motion of the sled and is given by the equation:
Force of friction = coefficient of friction * normal force
However, we need one more piece of information to calculate the force of friction accurately - the coefficient of friction between the sled and the snow. This information is not provided in the question. If the coefficient of friction is given, you can substitute its value into the equation and calculate the force of friction.