Question

3. A shelf hangs from the ceiling by two identical wires fixed to each end of the shelf.

The wires both make an angle of 25 degrees to the horizontal. The tension in each
wire is 80 N. What is the mass of the shelf? (Use g = 10 m/s^2 for this problem)
A 3.4 kg
B 6.8 kg
C 7.3 kg
D 14.4 kg

Answer 1

C. 7.3 kg

Step-by-step explanation:

The weight of the shelf can be calculated using the equation:

W = mg

where m is the mass of the shelf and g is the acceleration due to gravity (10 m/s^2).

Since the tension in each wire is equal and equal to 80 N, the total tension in the two wires is 80 N + 80 N = 160 N.

The horizontal component of the tension in each wire can be calculated using the equation:

T_horizontal = T * cos(25)

where T is the tension in each wire and 25 is the angle between the wire and the horizontal.

The horizontal component of the tension in each wire is equal to the weight of the shelf, so we can set the two equal:

T_horizontal = W

80 * cos(25) = W

W = 80 * cos(25) = 74.17 N

Finally, we can calculate the mass of the shelf using the equation for weight:

m = W / g

m = 74.17 / 10

m = 7.417 kg

Therefore, the mass of the shelf is approximately 7.417 kg, which is closest to option C, 7.3 kg.