Answer :
Final answer:
The magnitude of the force required to move a 126 kg block 20 meters in 5 seconds on a frictionless horizontal surface is 201.6 Newtons, calculated using Newton's second law of motion and the kinematic equations for constant acceleration.
Explanation:
To find the magnitude of the force F that causes a 126 kg block to move 20 m in 5 seconds on a frictionless horizontal surface, we'll use Newton's second law of motion and the kinematic equations. First, we assume constant acceleration since a constant force is applied. We will use the kinematic equation s = ut + 0.5at^2, where s is the displacement, u is the initial velocity (which is 0 m/s since the block starts from rest), a is the acceleration, and t is the time. We are given s = 20 m and t = 5 s. Plugging in the values, we get:
- 20 m = 0 m/s * 5 s + 0.5 * a * (5 s)^2
- a = 20 m / 0.5 / 25 s^2
- a = 1.6 m/s^2
Next, using Newton's second law, F = ma, and substituting the mass M = 126 kg and acceleration a = 1.6 m/s^2, we get:
- F = 126 kg * 1.6 m/s^2
- F = 201.6 N
Therefore, the magnitude of the force required to move the block 20 meters in 5 seconds is 201.6 Newtons.
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