A skier is pulled up a slope at a constant velocity by a tow bar. The slope is inclined at 27.2 ° with respect to the horizontal. The force applied to the skier by the tow bar is parallel to the slope. The skier's mass is 53.7 kg, and the coefficient of kinetic friction between the skis and the snow is 0.137. Find the magnitude of the force that the tow bar exerts on the skier.
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Fnormal=(Weight)(cos⊙)
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To find the magnitude of the force that the tow bar exerts on the skier, we need to analyze the forces acting on the skier.
First, let's determine the weight of the skier, which is the force of gravity acting on the skier. The weight can be calculated using the formula:
Weight = mass x gravitational acceleration
Weight = 53.7 kg x 9.8 m/s^2 ≈ 526.26 N
The weight is acting vertically downwards.
Next, we need to calculate the normal force, which is the force exerted by the slope perpendicular to it. The normal force cancels out the vertical component of the weight. The normal force can be calculated using the formula:
Fnormal = Weight x cos(θ)
where θ is the angle between the slope and the horizontal.
Fnormal = 526.26 N x cos(27.2°) ≈ 470.21 N
Here, θ = 27.2°.
Now, let's analyze the forces parallel to the slope. There are two forces acting parallel to the slope: the force applied by the tow bar and the force of kinetic friction.
The force of kinetic friction can be calculated using the formula:
Friction = coefficient of kinetic friction x Fnormal
Friction = 0.137 x 470.21 N ≈ 64.43 N
Since the skier is pulled up the slope at a constant velocity, the force applied by the tow bar must cancel out the force of kinetic friction. So, the magnitude of the force exerted by the tow bar on the skier is equal to the force of kinetic friction:
Force by tow bar = Friction ≈ 64.43 N
Therefore, the magnitude of the force that the tow bar exerts on the skier is approximately 64.43 N.