A skier speeds down a smooth ski slope which is at an angle of theta = 25 degree

Question

A skier speeds down a smooth ski slope which is at an angle of theta = 25 degree with the horizontal. The mass of the skier is 67 kg. Take the downhill direction to be positive and uphill to be negative. What net force is acting on the skier? (Indicate the direction with the sign of your answer.) what is the acceleration experienced by the skier? (indicate the direction with the sign of your answer.) How does the net force experienced by the skier change if the ski slope becomes steeper? Increases decreases remains the same The block In the figure below has a mass of 5.9 kg and It rests on an Incline of angle 6. you then push on the block with a force of F = 37 N, directed up the slope as shown. Assume the Incline is smooth and determine the angle of the incline if the block moves with constant speed.

Explanation / Answer

part a:

net force=component of weight of the skier along the incline=67*9.8*sin(25)=277.49 N

part b:

force along the slope=weight*sin(theta)

=277.49 N

so acceleration=force/mass=4.1416 m/s^2

part c:

as net force is directly proportional to sine of the inclination and sine increases as theta increases from 0 to 90 degrees,so if slope becomes steeper i.e. angle increases

then net force will increase.

Q2.

as block is moving with constant speed,

force F=component of weight along the incline

==>F=mass*g*sin(theta)

==>37=5.9*9.8*sin(theta)

==>theta=39.7856 degrees

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