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
M*g = 40*9.8 = 392 N. = Wt. of sled.
Fp = 392*sin 0 = 0 = Force parallel to the surface.
Fn = 392*Cos 0 = 392 N. = Force perpendicular to the surface.
Fs = u*Fn = 0.4 * 392 = 156.8 N. = Force
of static friction.
Fk = 0.25 * 392 N. = 98 N. = Force of kinetic friction.
a. Fap-Fs = M*a
Fap-156.8 = M*0
Fap = 156.8 N. = Force applied.
b. Fap-Fk = M*a
Fap-98 = M*0
Fap = 98 N.
c. Fap-Fk = M*a
Fap-98 = 40 * 3
Fap = 120 + 98 = 218 N.
To answer these questions, we need to understand the concepts of static and sliding friction and how they relate to force. Let's break it down step by step:
a) To start the sled moving, we need to overcome the static friction. The formula for static friction is:
F_static = μ_static * N
where F_static is the force of static friction, μ_static is the coefficient of static friction, and N is the normal force (equal to the weight of the sled).
In this case, the coefficient of static friction is given as 0.40. The normal force is equal to the weight of the sled, which can be calculated by multiplying the mass of the sled (40 kg) by the acceleration due to gravity (9.8 m/s^2). So, N = 40 kg * 9.8 m/s^2.
Using the formula, we can calculate the force needed to overcome static friction:
F_static = 0.40 * (40 kg * 9.8 m/s^2)
b) To keep the sled moving at a constant speed, we need to overcome the sliding friction. The formula for sliding friction is similar to static friction:
F_sliding = μ_sliding * N
where F_sliding is the force of sliding friction and μ_sliding is the coefficient of sliding friction.
In this case, the coefficient of sliding friction is given as 0.25. Again, we need to calculate the normal force N as explained in part a. Using the formula, we can calculate the force needed to overcome sliding friction:
F_sliding = 0.25 * (40 kg * 9.8 m/s^2)
c) Once the sled is moving, to accelerate it at 3.0 m/s^2 an additional force is required. This force is the net force acting on the sled. The net force is given by Newton's second law:
F_net = m * a
where F_net is the net force, m is the mass of the sled, and a is the desired acceleration.
In this case, the mass of the sled is given as 40 kg and the desired acceleration is 3.0 m/s^2. Using the formula, we can calculate the total force required to accelerate the sled:
F_net = 40 kg * 3.0 m/s^2
Keep in mind that these calculations assume ideal conditions, and there may be other factors to consider, such as air resistance or other forces acting on the sled.