D. Light from the sun is reflected off the moon's surface
Answer:
(a) 4.21 m/s
(b) 24.9 N
Explanation:
(a) Draw a free body diagram of the object when it is at the bottom of the circle. There are two forces on the object: tension force T pulling up and weight force mg pulling down.
Sum the forces in the radial (+y) direction:
∑F = ma
T − mg = m v² / r
v = √(r (T − mg) / m)
v = √(0.676 m (54.7 N − 1.52 kg × 9.8 m/s²) / 1.52 kg)
v = 4.21 m/s
(b) Draw a free body diagram of the object when it is at the top of the circle. There are two forces on the object: tension force T pulling down and weight force mg pulling down.
Sum the forces in the radial (-y) direction:
∑F = ma
T + mg = m v² / r
T = m v² / r − mg
T = (1.52 kg) (4.21 m/s)² / (0.676 m) − (1.52 kg) (9.8 m/s²)
T = 24.9 N
Answer:
1. Density = 1200[kg/m^3]; 2. Volume= 0.005775[m^3], mass= 15.59[kg]
Explanation:
1. We know that the density is defined by the following expression.
![Density = \frac{mass}{volume} \\where:\\mass=90[kg]\\volume=0.075[m^{3} ]\\density=\frac{90}{0.075} \\density=1200[\frac{kg}{m^{3} }]](https://tex.z-dn.net/?f=Density%20%3D%20%5Cfrac%7Bmass%7D%7Bvolume%7D%20%5C%5Cwhere%3A%5C%5Cmass%3D90%5Bkg%5D%5C%5Cvolume%3D0.075%5Bm%5E%7B3%7D%20%5D%5C%5Cdensity%3D%5Cfrac%7B90%7D%7B0.075%7D%20%5C%5Cdensity%3D1200%5B%5Cfrac%7Bkg%7D%7Bm%5E%7B3%7D%20%7D%5D)
2. First we need to convert the units to meters.
wide = 35[cm] = 35/100 = 0.35[m]
long = 11 [dm] = 11 decimeters = 11/10 = 1.1[m]
Thick = 15[mm] = 15/1000 = 0.015[m]
Now we can find the density using the expression for the density.
![density= \frac{mass}{volume} \\where:\\volume = wide*long*thick\\volume=0.35*1.1*0.015 = 0.005775[m^3]\\\\mass= density*volume = 2700*0.005775 = 15.59[kg]](https://tex.z-dn.net/?f=density%3D%20%5Cfrac%7Bmass%7D%7Bvolume%7D%20%5C%5Cwhere%3A%5C%5Cvolume%20%3D%20wide%2Along%2Athick%5C%5Cvolume%3D0.35%2A1.1%2A0.015%20%3D%200.005775%5Bm%5E3%5D%5C%5C%5C%5Cmass%3D%20density%2Avolume%20%3D%202700%2A0.005775%20%3D%2015.59%5Bkg%5D)
