a 35 kg child slides down a 26 degree incline. the coefficient of kinetic friction is 0.33. what is her speed after sliding for 2.5 seconds starting from rest?
Wc = M*g = 35*9.8 = 343 N.
Fp = 343*sin26 = 150.4 N. = Force parallel to the incline.
Fn = 343*Cos26 = 308.3 N. = Normal.
Fp-Fk = M*a.
150.4-0.33*308.3 = 35*a.
35a = 48.66.
a = 1.39 m/s^2.
V = Vo + a*t = 0 + 1.39*2.5 = 3.48 m/s.
To determine the speed of the child after sliding down the incline for 2.5 seconds, we need to use the principles of Newton's laws of motion and the concept of friction.
Step 1: Calculate the net force acting on the child.
The net force is the force that accelerates the child down the incline. It is given by the formula:
Net force = Weight component parallel to the incline - Friction force
The weight component parallel to the incline can be calculated using the formula:
Weight component parallel = Weight * sin(angle)
where the angle is 26 degrees.
Given:
Weight of the child (W) = 35 kg * 9.8 m/s² (acceleration due to gravity)
First, calculate the weight component parallel to the incline:
Weight component parallel = 35 kg * 9.8 m/s² * sin(26°)
Step 2: Calculate the friction force.
The friction force can be calculated using the formula:
Friction force = Coefficient of kinetic friction * Normal force
The normal force (Fn) can be calculated as:
Normal force (Fn) = Weight * cos(angle)
Given:
Coefficient of kinetic friction (μ) = 0.33
First, calculate the normal force:
Normal force (Fn) = 35 kg * 9.8 m/s² * cos(26°)
Then, calculate the friction force:
Friction force = 0.33 * Normal force
Step 3: Calculate the acceleration.
Using Newton's second law of motion, the acceleration (a) can be calculated as:
Acceleration (a) = Net force / Mass
Given:
Mass (m) = 35 kg
Acceleration (a) = Net force / Mass
Step 4: Calculate the final velocity.
The final velocity (v) can be determined using the following kinematic equation:
Final velocity (v) = Initial velocity (u) + (acceleration * time)
Given:
Initial velocity (u) = 0 m/s (starting from rest)
Time (t) = 2.5 seconds
Final velocity (v) = 0 + (acceleration * 2.5)
Now, let's calculate each step:
Step 1:
Weight component parallel = 35 kg * 9.8 m/s² * sin(26°)
Step 2:
Normal force (Fn) = 35 kg * 9.8 m/s² * cos(26°)
Friction force = 0.33 * Normal force
Step 3:
Acceleration (a) = (Weight component parallel - Friction force) / Mass
Step 4:
Final velocity (v) = 0 + (acceleration * 2.5)
Substituting the calculated values in each step will give us the final answer.