A massive steel cable drags a 15.0 kg block across a horizontal, frictionless surface. A 85.0 N force applied to the cable causes the block to reach a speed of 4.10 m/s in 1.90 s.
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4.10/1.90 = 2.16 is the acceleration im m/s^2
The product of mass and acceleration is 32.4 N, which is less than the applied force. If the surface is horizontal and frictionless, your numbers are inconsistent.
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To solve this problem, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. In this case, since the surface is frictionless, the force applied to the block is equal to the net force acting on it.
To find the acceleration of the block, we first need to find the net force acting on it. We can use the equation:
Net force = mass * acceleration
From the given information, we know that the mass of the block is 15.0 kg and the force applied to the cable is 85.0 N. Therefore, we can rewrite the above equation as:
85.0 N = 15.0 kg * acceleration
Now we can solve for the acceleration:
acceleration = 85.0 N / 15.0 kg
acceleration = 5.67 m/s^2
Now that we have the acceleration, we can find the distance travelled by the block using the equation:
distance = initial velocity * time + (1/2) * acceleration * time^2
From the given information, we know that the initial velocity of the block is 0 m/s (since it starts from rest), the time taken is 1.90 s, and the acceleration is 5.67 m/s^2. Plugging these values into the equation, we get:
distance = 0 m/s * 1.90 s + (1/2) * 5.67 m/s^2 * (1.90 s)^2
distance = (1/2) * 5.67 m/s^2 * (3.61 s^2)
distance = 5.67 m/s^2 * 1.8059 s^2
distance = 10.24 meters
Therefore, the block travels a distance of 10.24 meters when a force of 85.0 N is applied to the cable.