A child is sliding on a sled at 1.8 to the right. You stop the sled by pushing on it for 0.70 in a direction opposite to its motion.If the mass of the child and sled is 36 , what average force do you need to apply to stop the sled?
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To find the average force required to stop the sled, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass times the acceleration of the object.
First, let's determine the acceleration of the sled. Since the sled comes to a stop, the final velocity will be 0. We need to find the initial velocity and the deceleration.
Given:
- Initial velocity of the sled (v) = 1.8 m/s to the right
- Final velocity of the sled (vf) = 0 m/s
Applying the formula: vf = v + at, where a is the acceleration and t is the time, we rearrange it to solve for a:
0 = 1.8 + a * 0.70
Subtracting 1.8 from both sides of the equation, we get:
-1.8 = 0.7a
Dividing both sides by 0.7, we find:
a = -1.8 / 0.7
So, the sled experiences an acceleration of approximately -2.57 m/s² (negative because it's in the opposite direction of motion).
Now we can calculate the average force using Newton's second law. The formula is:
Force (F) = mass (m) * acceleration (a)
Given:
- Mass of the child and sled (m) = 36 kg
- Acceleration (a) = -2.57 m/s²
Substituting the values into the formula, we get:
F = 36 * (-2.57)
Simplifying the calculation:
F ≈ -92.52 N
The average force required to stop the sled is approximately 92.52 N in the direction opposite to its motion (to the left).