A toboggan (with a mass of 15.0 kg) is being pulled by two people who are each holding their own rope, horizontally with an angle 35 degrees off the direction of travel. They are each pulling with a force of 40.0 N, against a friction force of 20.0 N.
a) What is the net force?
b) What is the acceleration of the mass?
Resolve the forces to the direction of travel
F=2*40*cos(35)
=65.53 N
Fnet = 65.53-20
= 45.53 N
For acceleration, use Fnet = ma
a=Fnet/m
=45.53/15
= 3.03 m/s²
To find the net force acting on the toboggan, you need to consider the forces acting in the horizontal direction. In this case, there are two forces: the force applied by the people pulling the ropes and the friction force opposing the motion.
a) Net force is the vector sum of all the forces acting on the object, so we need to find the horizontal components of the forces. Each person is pulling with a force of 40.0 N at an angle of 35 degrees off the direction of travel. To find the horizontal component of each force, we can use trigonometry.
The horizontal component of each force is given by:
F_horizontal = F * cos(angle)
where F is the magnitude of the force and angle is the angle off the direction of travel.
For each person, the horizontal component of the force is:
F1_horizontal = 40.0 N * cos(35 degrees)
F2_horizontal = 40.0 N * cos(35 degrees)
Now, since the two people are pulling in the same direction, the net force is the sum of their individual forces' horizontal components:
Net force = F1_horizontal + F2_horizontal
b) The acceleration of the mass can be calculated using Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
The acceleration can be calculated using the equation:
acceleration = net force / mass
Now that we know the net force from part (a) and the mass of the toboggan (15.0 kg), we can calculate the acceleration.