The combined weight of a crate and dolly is 256N.
(a)If the person pulls on the rope with a constant force of 30.1N, what is the acceleration of the system (crate plus dolly)? Assume that the systems starts from rest and that there are no frictional forces opposing the motion of the systems. Answer in m/s square.
(b) How far will it move in 1.82 s?
This problem cannot be answered without a description of the system that includes the values of the masses involved.
To find the acceleration of the system, 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, F = ma.
In this case, the force the person applies by pulling the rope is 30.1N. To find the mass of the system (crate plus dolly), we need to convert the weight (256N) to mass by dividing it by the acceleration due to gravity (g).
Weight = mass x gravity
256N = mass x 9.8 m/s^2
mass = 256N / 9.8 m/s^2 ≈ 26.12 kg
Now we can substitute the mass and the force into Newton's second law:
30.1N = 26.12 kg x a
Solving for acceleration (a), we get:
a = 30.1N / 26.12 kg ≈ 1.152 m/s^2
(a) The acceleration of the system is approximately 1.152 m/s^2.
To find the distance the system will move in 1.82 seconds, we can use the kinematic equation:
d = v_i * t + (1/2) * a * t^2
Since the system starts from rest, the initial velocity (v_i) is zero. We already know the acceleration (a) from the previous part, and the time (t) is given as 1.82 s. Plugging the values into the equation, we get:
d = 0 * 1.82 + (1/2) * 1.152 * (1.82)^2
Simplifying the equation further:
d = (1/2) * 1.152 * 3.3124
d ≈ 1.9159 meters
(b) The system will move approximately 1.9159 meters in 1.82 seconds.