A 75.0-kg cross-country skier is climbing a 3.0o
slope at a constant speed of 2.00 m/s and
encounters air resistance of 25.0 N. Find his power output for work done against the gravitational
force and air resistance. (b) What average force does he exert backward on the snow to accomplish
this? (c) If he continues to exert this force and to experience the same air resistance when he
reaches a level area, how long will it take him to reach a velocity of 10.0 m/s?
Nam is ah jeeff
To find the power output for work done against the gravitational force and air resistance, we can use the formula:
Power = Force x Velocity
(a) Gravitational force:
The component of the gravitational force acting along the slope can be calculated using the formula:
Force_gravity = mass x acceleration_due_to_gravity x sin(theta)
Here, mass = 75.0 kg, acceleration_due_to_gravity = 9.8 m/s^2 (approx.), and theta = 3.0°.
Force_gravity = 75.0 kg x 9.8 m/s^2 x sin(3.0°)
Note: The sin(theta) accounts for the fact that the force of gravity acts slightly less along the slope.
(b) Air resistance:
The magnitude of the air resistance force can be found using the given value of 25.0 N.
Force_air_resistance = 25.0 N (given)
(c) Total force:
The total force exerted by the skier can be calculated by subtracting the air resistance force from the gravitational force component acting along the slope:
Total_force = Force_gravity - Force_air_resistance
(d) Power:
Now that we have the total force exerted by the skier and the constant speed, we can calculate the power using the formula:
Power = Total_force x Velocity
(e) Average force:
The average force exerted by the skier on the snow can be calculated using the formula:
Average_force = Total_force
(f) Time taken:
To find the time taken to reach a velocity of 10.0 m/s, we can use the equation of motion:
Final_velocity = Initial_velocity + (Acceleration x Time)
Since the acceleration is zero (constant speed), the equation simplifies to:
Final_velocity = Initial_velocity
Solving for time:
Time = (Final_velocity - Initial_velocity) / Acceleration
In this case, Initial_velocity = 2.00 m/s, Final_velocity = 10.0 m/s, and Acceleration = 0 (constant speed).
Now, let's calculate the values step by step.
Suc My COC and show vagine and bob
ker blam
is fat
force up: mg*SinTheta
power up=(mgSinTheta-25)velocity
b. force backward=force up+25
c. net force=ma
forceup-25=ma solve for a, then
vf=vi+2ad solve for d