🔭 physics

1. **State the problem:** Calculate how many hydrogen atoms are in the sun given that the mass of hydrogen in the sun is about $1.5 \times 10^{30}$ kilograms. 2. **Formula and cons

1. **State the problem:** We want to find the total mass of all the protons in Betelgeuse given the number of protons and the mass of one proton. 2. **Given:**

1. **State the problem:** We need to find the density of a piece of metal given its mass and the change in water volume when it is submerged. 2. **Formula used:** Density is calcul

1. **State the problem:** We need to find the speed of the boat between 30 and 50 seconds after starting using the distance-time graph. 2. **Recall the formula for speed:** Speed i

1. **Problem statement:** We want to find the time $t$ it takes for an object to fall from a height of 0.55 m under gravity. 2. **Formula used:** The vertical displacement under co

1. The problem is to understand the assumption about the vector \( \mathbf{G} \) being on the normal and whether this assumption is correct. 2. In many physics and engineering prob

1. **State the problem:** We have a cable from a pulley to a person's hand and from the pulley vertically down to a weight. The cable length from the person's hand to the weight is

1. **State the problem:** Calculate the average speed in km/h for a lap record on the Melbourne Formula 1 track, which is 5.303 km long, with a lap time of 1 minute and 24 seconds.

1. **Problem statement:** A soccer player kicks a ball at an initial velocity at an angle of 41° above the horizontal. The ball passes over a front wall 30.7 m away horizontally at

1. **State the problem:** We want to evaluate the expression $$\left[\frac{(1-\alpha) S}{4 \sigma}\right]^{1/4}$$ where $$\alpha = 0.3$$, $$S = 1361\ \text{W m}^{-2}$$, and $$\sigm

1. **State the problem:** We need to find the velocity at $3.5$ seconds from the given graphs. 2. **Identify the relevant graph:** Velocity is the rate of change of displacement wi

1. **Problem statement:** We have four penguins connected by cords on frictionless ice. Given masses $m_1=16$ kg, $m_3=20$ kg, $m_4=22$ kg, and tensions $T_2=134$ N, $T_4=234$ N, w

1. **State the problem:** We have two resistors in parallel with total resistance $R_T = 0.75$ ohms. One resistor $R_2$ is 2 ohms more than the other resistor $R_1$, so $R_2 = R_1

1. **State the problem:** A child slides down a playground slide starting from rest and reaches a speed of 4.5 m/s at the end of the slide, which is 2.8 m long. We need to find the

1. **State the problem:** A ball rolls at an initial velocity $v_0 = 11.5$ m/s along flat ground, then rolls up a hill for a distance $d = 11$ m before stopping. We need to find th

1. The problem is to convert an acceleration value from meters per minute squared to meters per second squared. 2. The given acceleration is $8$ meters per minute squared ($8\ \tex

1. **State the problem:** We need to estimate the air density $\rho$ in kg/m³ given the air temperature $T = 15^\circ C$, pressure $P = 1008$ hPa, and gas constant $R = 287$ J kg⁻¹

1. **Problem statement:** We have a block of mass $m=1500$ kg on an inclined plane at an angle $\theta=40^\circ$. A vertical downward force $W=2500$ N acts on the block. The coeffi

1. **Problem statement:** We have a block of mass 1500 kg on a 40° incline.

1. Let's understand the problem: You have a maximum power value $P_{max} = 23725.962$ Newtons (N). 2. The question "how did this happen?" suggests you want to know how this maximum

1. **Problem Statement:** We have a block of mass $m=1500$ kg on an inclined plane at angle $\theta=40^\circ$. A vertical downward force $W=2500$ N acts on the block. The coefficie