A skier of mass 40.6 kg comes down a slope
of constant angle 30◦ with the horizontal.
What is the force on the skier parallel to
the slope? Neglect friction. The acceleration
of gravity is 9.8 m/s
2
the component of gravitational acceleration parallel to the slope is
___ g sin(30º)
the force on the skier is
___ m g sin(30º)
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To find the force on the skier parallel to the slope, we need to break down the gravitational force into its components. The force parallel to the slope is the force that accelerates the skier down the slope.
First, we find the component of the gravitational force parallel to the slope. The gravitational force acting on the skier is given by the formula:
F_gravity = mass × acceleration due to gravity
Substituting the given values, we have:
F_gravity = 40.6 kg × 9.8 m/s^2
F_gravity = 398.68 N
Next, we calculate the force parallel to the slope. Since the slope is inclined at an angle of 30 degrees with the horizontal, we need to find the component of the gravitational force parallel to the slope. This can be calculated using the formula:
Force parallel to slope = F_gravity × sin(angle)
Substituting the values, we have:
Force parallel to slope = 398.68 N × sin(30 degrees)
Force parallel to slope = 398.68 N × 0.5
Force parallel to slope = 199.34 N
Therefore, the force on the skier parallel to the slope is 199.34 N.