Question

a 47 - n box is pulled along a frictionless horizontal surface by a 25 - n weight hanging from a cord on a frictionless pulley.
a. what is the boxs mass?
b. what is the weightss mass?
c. what is the boxs acceleration?
d. what is the magnitude of the force exerted on the cord?

Explanation:

Step1: Calculate the box's mass (a)

Using the formula \(F = mg\) (where \(F\) is weight, \(m\) is mass, \(g = 9.8\ m/s^{2}\)). Rearranging for \(m\), we get \(m=\frac{F}{g}\). Substituting \(F = 47\ N\), \(m=\frac{47}{9.8}\approx4.8\ kg\).

Step2: Calculate the weight's mass (b)

Using \(F = mg\) again. Given \(F = 25\ N\), \(m=\frac{25}{9.8}\approx2.6\ kg\).

Step3: Calculate the system's acceleration (c)

The net force \(F_{net}=25\ N\) (weight of the hanging mass). The total mass \(m_{total}=4.8 + 2.6=7.4\ kg\). Using \(F = ma\), so \(a=\frac{F_{net}}{m_{total}}=\frac{25}{7.4}\approx3.4\ m/s^{2}\).

Step4: Calculate the force exerted on the cord (d)

For the box, \(F = ma\). \(m = 4.8\ kg\), \(a = 3.4\ m/s^{2}\). So \(F=4.8\times3.4 = 16.3\ N\).

Answer:

a. \(4.8\ kg\)
b. \(2.6\ kg\)
c. \(3.4\ m/s^{2}\)
d. \(16.3\ N\)