a sled weighing 100lb reaches the foot of a hill with a speed of 40ft/s.The coefficient of kinetic friction between the led and the horizontal surface of the ice at the foot of the hill is 0.030.
To find the acceleration of the sled on the ice, we can use Newton's second law of motion, which states:
Force = mass × acceleration
First, let's calculate the force of kinetic friction acting on the sled. The formula for the force of friction is:
Force of friction = coefficient of friction × normal force
The normal force is equal to the weight of the sled, which is the force due to gravity. So, the normal force is 100 pounds or 100 lb.
Normal force = weight = mass × acceleration due to gravity
Since the sled weighs 100 pounds, we need to convert it to mass using the conversion factor 1 lb = 0.4536 kg:
Mass = 100 lb × (0.4536 kg / 1 lb) = 45.36 kg
Acceleration due to gravity is approximately 9.8 m/s².
Now we can calculate the normal force:
Normal force = 45.36 kg × 9.8 m/s² = 444.528 N
Next, let's calculate the force of friction:
Force of friction = 0.030 × 444.528 N = 13.33784 N
Since the sled is moving on a horizontal surface, the force of friction acts in the opposite direction of motion. So, the net force acting on the sled is:
Net force = force of friction = 13.33784 N
Now, we can use Newton's second law of motion to find the acceleration:
13.33784 N = 45.36 kg × acceleration
Dividing both sides by the mass of the sled, we get:
acceleration = 13.33784 N / 45.36 kg = 0.293 m/s²
Therefore, the acceleration of the sled on the ice is 0.293 m/s².