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An ice shed has a mass of 253 kg and slides without friction on a frozen lake. Bob pushes on the shed with a force of 99.9 N to the West. Hank pushes with a force of 75.8 N in the direction 65.0° North of West. What is the magnitude of the acceleration of the shed?

a) 0.395 m/s²
b) 0.678 m/s²
c) 0.588 m/s²
d) 0.299 m/s²
e) 0.694 m/s²

Answer :

Final answer:

The magnitude of the acceleration of the shed is 0.583 m/s^2.

Explanation:

To calculate the magnitude of the acceleration of the shed, we need to find the net force acting on it. The net force is the vector sum of all the forces acting on the shed.

First, let's break down the forces into their components. Bob's force is directed to the West, so its x-component is -99.9 N. Hank's force is directed 65.0∘ North of the West, so its x-component is -75.8 N * cos(65.0∘) and its y-component is -75.8 N * sin(65.0∘).

The x-component of the net force is the sum of the x-components of the individual forces:

-99.9 N + (-75.8 N * cos(65.0∘)) = -99.9 N - 30.9 N = -130.8 N

The y-component of the net force is the sum of the y-components of the individual forces:

-75.8 N * sin(65.0∘) = -75.8 N * 0.9063 = -68.8 N

Now, we can calculate the magnitude of the net force using the Pythagorean theorem:

Net force = sqrt((-130.8 N)^2 + (-68.8 N)^2) = sqrt(17100.64 N^2 + 4733.44 N^2) = sqrt(21834.08 N^2) = 147.7 N

Finally, we can calculate the acceleration using Newton's second law of motion:

Acceleration = Net force / Mass = 147.7 N / 253 kg = 0.583 m/s^2

Learn more about calculating the acceleration of an object on a frictionless surface here:

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