The coefficients of friction between a 250 lb football sled and the grass are Mu(s)=0.6 and Mu(k)=0.4. For grass and cleats, Mu(s)=0.9. One 280 lb tryout exerts a horizontal push of 140 lb on the sled. What is the acceleration of the sled?
To find the acceleration of the sled, we will use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
First, let's break down the forces acting on the sled:
1. Normal force (N): This is the force exerted by the surface (grass) on the sled perpendicular to the surface. In this case, the normal force is equal to the weight of the sled, which is 250 lb.
2. Force of friction (Ff): The force of friction can have two components, static friction (Fs) and kinetic friction (Fk), depending on whether the sled is at rest or in motion.
- If the sled is at rest or not moving, we will use the coefficient of static friction (µs).
- If the sled is in motion, we will use the coefficient of kinetic friction (µk).
Now, let's calculate the forces:
1. Calculate the force of friction (Ff) using the static friction coefficient (µs) when the sled is at rest:
Ff = µs * N
Since µs = 0.6 and N = 250 lb, we can calculate Ff:
Ff = 0.6 * 250 lb
Ff = 150 lb
2. Determine if the force exerted by the tryout (140 lb) is enough to overcome the static friction (Ff) and set the sled in motion. If the force exerted exceeds the force of static friction, it will start moving. If not, the sled will remain at rest.
3. Since the force exerted by the tryout is 140 lb, which is greater than the force of static friction (150 lb), the sled will start moving. Now we need to calculate the force of kinetic friction (Fk) using the kinetic friction coefficient (µk):
Fk = µk * N
Since µk = 0.4 and N = 250 lb, we can calculate Fk:
Fk = 0.4 * 250 lb
Fk = 100 lb
4. Now, let's calculate the net force acting on the sled:
Net force (Fnet) = Force exerted by the tryout - Force of kinetic friction
Fnet = 140 lb - 100 lb
Fnet = 40 lb
5. Finally, we can calculate the acceleration (a) of the sled using Newton's second law:
Fnet = ma
Since the mass of the sled (m) is given as 280 lb, we can rearrange the equation to solve for acceleration:
a = Fnet / m
a = 40 lb / 280 lb
a ≈ 0.143
Therefore, the acceleration of the sled is approximately 0.143 ft/s².