A person exerts a force of 90 N on a rope that pulls a sled across a very smooth surface. The rope is oriented 37∘ above the horizontal. The sled has a total mass of 40 kg . The sled starts at rest and moves for 10 m.
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To find the acceleration of the sled, 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 multiplied by its acceleration.
In this case, the force exerted on the sled is 90 N, and the mass of the sled is 40 kg. The force applied to the sled can be broken down into two components: the horizontal component and the vertical component.
The vertical component of the force does not contribute to the horizontal motion of the sled since the surface is very smooth. Therefore, we can ignore the vertical component and only consider the horizontal component.
To find the horizontal component of the force, we can use trigonometry. The horizontal component of the force can be calculated using the equation:
horizontal force = applied force * cos(angle)
In this case, the applied force is 90 N, and the angle is 37 degrees. Plugging the values into the equation, we get:
horizontal force = 90 N * cos(37 degrees)
Using a calculator, we find that the horizontal force is approximately 72.5 N.
Now, we can plug this value into Newton's second law to find the acceleration of the sled:
net force = mass * acceleration
72.5 N = 40 kg * acceleration
Dividing both sides of the equation by 40 kg, we can isolate the acceleration:
acceleration = 72.5 N / 40 kg
Calculating this equation gives us an acceleration of approximately 1.81 m/s².
Therefore, the sled has an acceleration of 1.81 m/s².