A skier wants to build a rope tow to pull herself up a ski hill that is inclined at 15 with the horizontal. Calculate the tension needed in the rope to give the skier's 54kg body a 1.2 m/s^2 acceleration.

tuleg

M*g = 54 * 9.8 = 529.2 N. = Wt. of skier.

Fp = 529.2*sin15 = 137 N. = Force parallel to the hill.

Fn = 529.2*Cos15 = 511 N. = Normal force.

Fap-Fp = M*a.
Fap-137 = 54*1.2,
Fap = 201.8 N. = Applied force = Tension in rope.

Well, Mr. Skier, it looks like you want to play a little tug-of-war with gravity, huh? Don't worry, I'll crunch some numbers for you.

First things first, let's break down the forces at play here. We've got the tension in the rope and the skier's weight pulling her down the hill. The force of gravity can be calculated by multiplying her mass (54 kg) by the acceleration due to gravity (9.8 m/s^2), which gives us a downward force of approximately 529.2 N.

Now, let's deal with the acceleration. To calculate the force required to accelerate the skier at 1.2 m/s^2, we multiply her mass by the acceleration, which gives us approximately 64.8 N.

Since the skier is on an inclined slope, we need to consider the component of the gravitational force acting parallel to the slope. This force can be determined by multiplying the total gravitational force (529.2 N) by the sin of the angle of inclination (15 degrees), giving us a force of about 137.5 N.

To find the tension needed in the rope, we need to add the force required to accelerate the skier (64.8 N) to the force parallel to the slope (137.5 N). So, the total tension needed in the rope is around 202.3 N.

So there you have it, Mr. Skier! You'll need a tension of approximately 202.3 N in that rope to give you a sweet acceleration of 1.2 m/s^2. Just make sure to hold on tight and don't let gravity pull you down too much, or you might end up skiing on your head!

To calculate the tension needed in the rope, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object times its acceleration.

Step 1: Calculate the force due to gravity
The force due to gravity (weight) is given by the formula:
Force = mass × acceleration due to gravity

The acceleration due to gravity is approximately 9.8 m/s^2.

Force due to gravity = 54 kg × 9.8 m/s^2 = 529.2 N

Step 2: Resolve the force into two components
The force can be resolved into two components: the component that acts perpendicular to the incline (normal force) and the component that acts parallel to the incline (force parallel to the incline).

The component perpendicular to the incline (normal force) is equal to the force due to gravity:

Normal force = 529.2 N

The component parallel to the incline (force parallel to the incline) is equal to:

Force parallel to the incline = Force due to gravity × sin(angle of incline)

In this case, the angle of the incline is 15°. So, we can calculate:

Force parallel to the incline = 529.2 N × sin(15°) = 137.6 N

Step 3: Calculate the tension in the rope
The tension in the rope is equal to the force parallel to the incline, since it is required to provide the necessary force to accelerate the skier up the hill.

Therefore, the tension needed in the rope is 137.6 N.

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