Calculate the magnitude of each force acting on the sleigh. The friction force has a magnitude of 4000N. The sleigh has a mass of 200kg. The people and their luggage have a mass of 300kg. The harness makes a 20-degree angle with the horizontal. Assume the sleigh is moving at a constant speed. Use g=10m/s^2.
constant speed means pull force = drag force
if harness tension = T
then Pull force = T cos 20
Pull force - friction force = m a = 0
so
T cos 20 = 4000
up force from tension = T sin 20
there is no acceleration up
weight = m g = (200+300)(10) = 5000 N
net force up from snow = weight - tension component up = 5000 - T sin 20
To calculate the magnitude of each force acting on the sleigh, we need to consider the forces that are present. The forces acting on the sleigh are the gravitational force (weight) and the frictional force.
1. Gravitational Force (Weight):
The gravitational force acting on an object can be calculated using the formula:
Weight = mass * acceleration due to gravity
In this case, the mass of the sleigh is given as 200 kg. The mass of the people and their luggage is given as 300 kg. So the total mass of the system is 200 kg + 300 kg = 500 kg.
The acceleration due to gravity, denoted as "g", is given as 10 m/s^2.
Using the formula, we can calculate the weight:
Weight = mass * g = 500 kg * 10 m/s^2 = 5000 N
Therefore, the gravitational force acting on the sleigh is 5000N.
2. Frictional Force:
The frictional force acting on the sleigh has a magnitude of 4000N, as given in the problem statement.
Since the sleigh is moving at a constant speed, we know that the net force acting on the sleigh is zero. This means that the frictional force must be equal in magnitude and opposite in direction to the weight of the system.
Therefore, the magnitude of each force acting on the sleigh is as follows:
- Gravitational force = 5000N (downward)
- Frictional force = 4000N (opposite to the direction of motion)
Note: The given information about the harness angle is not directly necessary for calculating the magnitudes of the forces. It is only useful if you need to find the horizontal component of the tension force in the harness.