Sam, whose mass is 80kg , takes off across level snow on his jet-powered skis. The skis have a thrust of 220N and a coefficient of kinetic friction on snow of 0.1. Unfortunately, the skis run out of fuel after only 8.0s .
To determine the distance that Sam travels before running out of fuel, we need to break down the problem into several steps.
Step 1: Find the net force acting on Sam.
The net force can be determined using the formula:
Net force = Thrust - Frictional force
Given:
Thrust (T) = 220 N
Coefficient of kinetic friction (μ) = 0.1
Frictional force (F_friction) can be calculated using the formula:
F_friction = μ * Normal force
The normal force (F_normal) is equal to the weight (mg), where m is the mass of Sam and g is the acceleration due to gravity (9.8 m/s^2).
F_friction = μ * mg
Net force = Thrust - F_friction
Step 2: Calculate the acceleration of Sam.
Using Newton's second law of motion:
Net force = mass * acceleration
Therefore,
acceleration = Net force / mass
Step 3: Determine the distance traveled by Sam.
Given that the skis run out of fuel after 8.0 seconds, we can use the kinematic equation:
distance = initial velocity * time + (1/2) * acceleration * time^2
Initially, Sam is at rest, so the initial velocity is zero.
Now, let's calculate the values needed to solve the problem.
First, calculate the frictional force acting on Sam:
F_friction = μ * mg
F_friction = 0.1 * 80 kg * 9.8 m/s^2
Next, calculate the net force:
Net force = Thrust - F_friction
Net force = 220 N - F_friction
Now, calculate the acceleration:
acceleration = Net force / mass
Finally, calculate the distance traveled by Sam:
distance = 0.5 * acceleration * time^2
Substitute the values and calculate the distance.