A sled mass of 40 kg is pulled along a snow covered surface. The coefficient of static friction is 0.40 and the coefficient of sliding friction is 0.25
a) what force is needed to start the sled moving?
b)what force is needed to start to keep the sled moving at a constant speed?
c) once moving, what total force must be applied to the sled to accelerate it at 3.0 m/s2
To solve these questions, we can use the equations related to friction and Newton's laws of motion.
a) To start the sled moving, we need to overcome the static friction. The force needed to overcome static friction is given by:
F_static = μ_s * N
where F_static is the force of static friction, μ_s is the coefficient of static friction, and N is the normal force.
The normal force is equal to the weight of the sled, which can be calculated as:
N = m * g
where m is the mass of the sled and g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the values, we have:
N = 40 kg * 9.8 m/s² = 392 N
Now, we can calculate the force needed to start the sled moving:
F_static = 0.40 * 392 N = 156.8 N
Therefore, the force needed to start the sled moving is approximately 156.8 Newtons.
b) To keep the sled moving at a constant speed, we need to overcome the sliding friction. The force needed to overcome sliding friction is given by:
F_sliding = μ_slide * N
where F_sliding is the force of sliding friction, μ_slide is the coefficient of sliding friction, and N is the normal force.
Using the same values we calculated earlier, we have:
F_sliding = 0.25 * 392 N = 98 N
Therefore, the force needed to keep the sled moving at a constant speed is approximately 98 Newtons.
c) To calculate the total force needed to accelerate the sled at 3.0 m/s², we need to consider both the sliding friction force and the force required for acceleration.
The force required for acceleration can be calculated using Newton's second law of motion:
F_acceleration = m * a
where F_acceleration is the force required for acceleration, m is the mass of the sled, and a is the acceleration.
Substituting the values, we have:
F_acceleration = 40 kg * 3.0 m/s² = 120 N
Now, to find the total force, we need to consider both the sliding friction force and the force required for acceleration:
Total force = F_acceleration + F_sliding
Substituting the values, we have:
Total force = 120 N + 98 N = 218 N
Therefore, the total force required to accelerate the sled at 3.0 m/s² is approximately 218 Newtons.